Upcoming hollywood movies

 1)  Annabelle:Creation
       

                                       

                                          Director : David F. Sandberg                                   

                                          Release Date : 18 August,2017  

                                         producer : James wan, Peter Safran

                                             

                                            It is a upcoming american horror movie directed by David Sandberg and produced by  James wan.

                   

 2)  Kingsman : The Golden Circle

                                             

                                                 

                                          

                                      Director : Matthew vaughn                                  

                                     Release Date : 22 September,2017   

                                     producer : Adam Bohling, David Reid

                                   

                                                         It is upcoming british-american action comedy spy film directed by Matthew vaughn and the sequel to 2014 film kingsman.

3)  American Made
                              

                                             

                                       Director : Doug Liman                                     

                                      Release Date : 29 September,2017 

                                      producer : Doug Davison, Kim Roth

                                                      It is an upcoming biographical crime film directed by Doug Liman written by Garry Spinelli.

4) Flatliners

                         

                              

                                               Director : Niels Arden Oplev

                                               Release Date : 29 September,2017    

                                              producer : Peter Safran , Laurence Mark

                                                       It is upcoming american science psychological horro film directed by niels oplev and written by Ben Ripley.

5) The Snowman

                                            

                                              

                                        Director : Tomas Alfredson                                    

                                       Release Date : 13 October,2017

                                       producer : Robyn Solvo,Peter Gustafsson

                                              It is an upcoming british crime thriller horror film directed by Tomas Alfredson and written by Hossein Amini.

6) Geostorm

                                

                                        Director : Dean Devlin                                     

                                        Release Date : 20 October,2017   

                                        producer : David Ellison,Dana Goldberg

                                              It is an upcoming american enviornmental disaster science friction action film directed by Dean Devlin and written by Paul Guyot.

7) Blade Runner 2049

                                               

                                            

                                         Director : Denis Villeneuve                   

                                        Release Date : 6 October,2017    

                                        producer : Bud yorkin,Andrew Kosove

                                              It is an upcoming american neo noir science friction film directed by Denis Villeneuve and written by Michael Green .

                                            

Probability Formulas

                

1. Experiment

 An operation which can produce well-defined outcomes is called an experiment.

2. Random Experiment

If all the possible outcomes of an experiment are known but the exact output cannot be predicted in advance, that experiment is called a random experiment.

Examples

1. Tossing a fair coin
   When we toss a coin, the outcome will be either Head (H) or Tail (T)
2. Throwing an unbiased die
   Die is a small cube used in games. It has six faces and each of the six faces shows a different number of dots from 1 to 6. Plural of die is dice.
   When a die is thrown or rolled, the outcome is the number that appears on its upper face and it is a random integer from one to six, each value being equally like.
3. Drawing a card from a pack of shuffled cards
   A pack or deck of playing cards has 52 cards which are divided into four categories as given below
   1. Spades 
   2. Clubs 
   3. Hearts 
   4. Diamonds 
   Each of the above mentioned categories has 13 cards, 9 cards numbered from 2 to 10, an Ace, a King, a Queen and a jack
   Hearts and Diamonds are red faced cards whereas Spades and Clubs are black faced cards.
   Kings, Queens and Jacks are called face cards.

3. Sample Space

      When we perform an experiment,then the set of all possible outcome is called Sample space.      >It is denoted by 'S'.

Examples

1. When a coin is tossed, S = {H, T} where H = Head and T = Tail
2. When a dice is thrown, S = {1, 2 , 3, 4, 5, 6}
3. When two coins are tossed, S = {HH, HT, TH, TT} 

4. Probability Of Event

Let E be an event and S be the sample space. Then probability of the event E can be defined as

P(E) = n(E)n(S)

where P(E) = Probability of the event E, n(E) = number of ways in which the event can occur and n(S) = Total number of outcomes possible.

5. Results On Probability

i.  P(S)=1

ii. 0<_P(E)<

_1

iii. P(A U B) = P(A) + P(B) – P(A ∩

B)

iv. P(A¯)

= 1 - P(A)

Problems On area

Problems On Area

     1.  The difference between length and                  breadth of a rectangle is 23m.If a                    perimeter is 206 m, then it's area is:

Answer:   we have (l-b)=23 and 2(l+b)=206

                  Solving two equations we get                           :l=63,                b=40

 Hence, Area =(l*b)=63*40=2520m*m

Multiplication Short-cut Tricks

Multiplication of Two digit numbers:

1.   13 x 13 = ?

Answer: The result of multiplication of two digit number is 13×13 = 169.
Step 1: Multiply 3×3 = 9 then,
Step 2: Do Cross-multiplication (1×3) = 3 and (1×3) = 3.
Step 3: Add both the result (1×3 + 1×3) = 6 and write down to the left of 9 (result of step 1).
Step 4: Multiply left hand side numbers (1×1) = 1 and write down to the left of 6 (result of step 3).
Finally the result we get 169. (Try to calculate all four steps in mind.)


2.  87 x 33 = ?

The result of multiplication of two digit Answer: number is 88 x 33 = 2871
Step 1: Multiply (3×7) = 21 note down 1 and carry 2 then,
Step 2: Do Cross-multiplication (3×8) = 24 and (3×7) = 21.
Step 3: Add both the result with carry (24 + 21 + 2) = 47 and write down 7 carry 4.
Step 4: Multiply left hand side numbers (3×8) = 24 and add carry (24 + 4) write down to the left of 7
Finally the result we get 2871. (Try to calculate all four steps in mind.)


3.  17 x 19 = ?

Answer: The result of multiplication of two digit number is 17×19 = 323.
Step 1: Multiply 7×9 = 63 (note down 3 and carry over 6).
Step 2: (1×9 + 1×7 + 6 (add carry)) = 22 (note down 2 and carry over 2 for next step).
Step 3: (1×1 + 2) = 3, note it down.
And finally the result we get 323. (Try to calculate all three steps in mind.)



4.  38 x 27 = ?

Answer: The result of multiplication of two digit number is 38 x 27 = 1026
Step 1: Multiply (7×8) = 56 note down 6 and carry 5 then,
Step 2: Do Cross-multiplication (7×3) = 21 and (2×8) = 16.
Step 3: Add both the result with carry (21 + 16 + 6) = 42 and write down 2 carry 4.
Step 4: Multiply left hand side numbers (2×3) = 6 and add carry (6 + 4) write down to the left of 2
Finally the result we get 1026. (Try to calculate all four steps in mind.)



5.  59 x 42 = ?

Answer: The result of multiplication of two digit number is 59 x 42 = 2478
Step 1: Multiply (2×9) = 18 note down 8 and carry 1 then,
Step 2: Do Cross-multiplication (2×5) = 10 and (4×9) = 36.
Step 3: Add both the result with carry (10 + 36 + 1) = 47 and write down 7 carry 4.
Step 4: Multiply left hand side numbers (4×5) = 20 and add carry (20 + 4) write
down to the left of 7
Finally the result we get 2478. (Try to calculate all four steps in mind.)

Multiplication of a Three digit numbers

1.  175 x 157 = ?

Answer: The result of multiplication of three digit number is 175×157 = 27475.
Step 1: Multiply (5×7) = 35 (note down 5 carry 3).
Step 2: Then do cross multiplication (7×7 + 5×5 + 3 (add carry)) = 77 (note down 7 carry 7).
Step 3: Again (1×7 + 1×5 + 7×5 + 7 (add carry)) = 54 (note down 4 carry 5).
Step 4: do cross multiplication and add carry (1×5 + 1×7 + 5 (add carry)) = 17 (note down 7 carry 1).
Step 5: Again (1×1 + 1) = 2, note it down.
And finally the result we get 27475.



2.  275×354 = ?

Answer: The result of multiplication of three digit number is 275×354 = 97350.
Step 1: Multiply (4×5) = 20 (note down 0 carry 2).
Step 2: Then do cross multiplication (5×5 + 4×7 + 2 (add carry)) = 55 (note down 5 carry 5).
Step 3: Again (4×2 + 3×5 + 5×7 + 5 (add carry)) = 63 (note down 3 carry 6).
Step 4: Again do cross multiplication and add carry (5×2 + 3×7 + 6) = 37 (note down 7 carry 3).
Step 5: do multiplication of left numbers and add carry  (3×2 + 3) = 9, note it down.
And finally the result we get 97350.


3.  395×284 = ?

Answer: The result of multiplication of three digit number is 395×284 = 112180.
Step 1: Multiply (4×5) = 20 (note down 0 carry 2).
Step 2: Then do cross multiplication(4×9 + 8×5 + 2 (add carry)) = 78 (note down 8 carry 7).
Step 3: Again (4×3 + 2×5 + 8×9 + 7 (add carry)) = 101 (note down 1 carry 10).
Step 4: Again do cross multiplication and add carry (8×3 + 2×9 + 10) = 52 (note down 2 carry 5).
Step 5: do multiplication of left numbers(2×3 + 5) = 11, note it down.
And finally the result we get 112180.

Simple Interest solved Problems with tricks

SIMPLE INTEREST 

1. A sum of Rs.550 was taken a loan. This is to be repaid in two equal annual instalments. If the rate of interest be 20% compounded annually, then the value of each instalment is :

Answer: Rs. 360
Explanation:
Let the value of each instalment be Rs.x.
[ x / ( 1 + ( 20 / 100 ) ) ] + [ x / ( 1 + ( 20 / 100 ) )2 ] = 550
( 5x / 6 ) +( 25x / 36 ) = 550
x = Rs. 360


2. If the simple interest on Rs. 1120 for 2 years is Rs.8000/-, what is the rate of interest percent per annum?

Answer: 7%
Explanation:
Interest = Rs. 1120
Time = 2 years
Principle = Rs. 8000
Simple interest = [ ( Principle * Time * Rate ) / 100 ]
Rate = ( Simple interest * 100 ) / ( P * T )
Rate = ( 1120 * 100 ) / ( 8000 * 2 )
Rate = 56 / 8
= 7%


3. The simple interest on Rs. 1820 from March 9, 2003 to May 21, 2003 at [ 7 * ( 1 / 2 ) ]% rate?

Answer: Rs. 27.3
Explanation:
Time = ( 22 + 30 + 21 ) days
= 73 days
Rate = [ 7 * ( 1 / 2 ) ]%
= ( 15 / 2 )%
= ( 1 / 5 ) years ( ∴ 73 / 365 = 1 / 5 )
Simple Interest = ( principal * rate * time ) / 100
= [ 1820 * ( 15 / 2 ) * ( 1 / 5 ) ] / 100
= ( 1820 * 15 * 1 ) / ( 2 * 5 * 100 )
= 273 / 10
= Rs. 27.3


4. The difference between the interests received from two different banks on Rs. 500 for 2 years, is Rs. 2.50. Find the difference between their rates?

Answer: 0.25
Explanation:
Let the rates be x% and y%.
⇒ [ ( 500 * x * 2 ) / 100 ] - [ ( 500 * y * 2 ) / 100 ) ] = 2.5
⇒ ( 1000x / 100 ) - ( 1000y / 100 ) = 2.5
⇒ 10x - 10y = 2.5
⇒ 10 ( x - y ) = 2.5
x - y = 2.5 / 10
x - y = 0.25


5. A certain sum of money at simple interest amounts to Rs.1260 in 2 years and to Rs.1350 in 5 years. Find the rate percent per annum?

Answer: 2.5%
Explanation:
Simple Interest for 3 years = Rs.( 1350 - 1260 ) / 3
= Rs. 90 /3
= Rs. 30 Simple Interest for 2 years = Rs.[ ( 30 ) * 2 ]
= Rs. 60
Sum = Rs.( 1260 - 60 )
= Rs. 1200
Rate = ( 100 * 60 ) / ( 1200 * 2 )
= 5 / 2
= 2.5%


6. How much time will it take for an amount of Rs. 900 to yield Rs. 81 as interest at 4.5% per annum of simple interest?

Answer: 2 years
Explanation:
Principal = Rs. 900
Simple Interest = Rs. 81
Rate = 4.5 %
Time = ( 100 * Simple Interest ) / ( Principal * Rate )
= ( 100 * 81 ) / ( 900 * 4.5 )
= 8100 / 4050
= 2 years


7. A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. Find the sum?

Answer: Rs. 698
Explanation:
Simple Interest for 1 year = Rs. ( 854 - 815 )
= Rs. 39
Simple Interest for 3 years = Rs. ( 39 * 3 )
= Rs. 117
Principal = Rs. ( 815 - 117 )
= Rs. 698


8. A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9 percent per annum in 5 years. What is the sum?

Answer: Rs. 8925
Explanation:
Principal = ( 100 * Simple Interest ) / ( Rate * Time)
= Rs. [ ( 100 * 4016.25 ) / ( 9 * 5 ) ]
= Rs. ( 401625 / 45 )
= Rs. 8925


9. How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?

Answer: 4 years
Explanation:
Time = ( 100 * Simple Interest ) / ( Principal * Rate )
= ( 100 * 81 ) / ( 450 * 4.5 ) years
= 4 years


10. A sum of Rs. 800 amount to Rs. 920 in 3 years at simple interest. If the interest rate is increased by 3%, it would amount to how much?

Answer: Rs. 992
Explanation:
Simple Interest = Rs. ( 920 - 800 ) = Rs. 120
Principal = Rs. 800
Time = 3 years
Rate = ( 100 * Simple Interest ) / ( Principal * Time )
= [ ( 100 * 120 ) / ( 800 * 3 ) ] %
= 5%
New Rate = ( 5 + 3 ) %
= 8 %
New simple Interest = ( Principal * Rate * Time ) / 100
= Rs. [ ( 800 * 8 * 3 ) / 100 ]
= Rs. ( 8 * 8 * 3 )
= Rs. 192
New amount = Rs. ( 800 + 192 )
= Rs. 992

Simple Interest solved Problems

Simple Interest

1. Sahil took a loan for 6 years at the rate of 5% per annum on Simple Interest. If the total interest paid was Rs. 1230. Find the principal?

Answer: 4100
Explanation:
Simple Interest = ( Princeple * Rate * Time ) / 100
Principle = ( Simple Interest * 100 ) / ( R * T )
P = ( 1230 * 100 ) / ( 6 * 5 )
P = 4100.

2. A person took some amount with some interest for 2 years, but increase the interest for 1%, he paid Rs.120 extra, then how much amount he took?

Answer: Rs. 6000
Explanation:
2 years = Rs. 120
year = 120 / 2
Rate of Interest = 1%
= ( 100 / 1 ) * ( 120 / 2 )
P = Rs. 6000.


3. A borrow took by a man, for every 5 years it will be doubled, then what is the rate of the interest?

Answer: 20%
Explanation:
Principle = 1
Interest = 1
Time = 5 years
Rate = ?
Interest = ( Principle * Time * Rate ) / 100
1 = ( 1 * 5 * R ) / 100
R = 20%.


4. What is the interest earned by Raj on an amount of Rs.15000 in 10 months at 5 p.c.per annum?

Answer: Rs. 625
Explanation:
Interest = ( Principle * Rate of interest * Time ) / 100
= ( 15000 * 10 * 5 ) / ( 100 * 12 )
= Rs. 625.


5. A man invested Rs. 4940 in Rs. 10 shares quoted at Rs. 9.50. If the rate of dividend be 14%, Find the annual income?

Answer: Rs. 728
Explanation:
Market Value of a share = Rs. 9.50
Investment = Rs.4940
Number of shares = 4940 / 9.50
= 520
Face Value of a share = Rs. 10
Dividend = 14%
Dividend per share = ( 10 * 14 ) / 100
= Rs. 1.4
His annual income = 520 * 1.4
= Rs. 728.


6. What would be the simple interest obtained on an amount of Rs. 9850 at the rate of 7 p.c.per annum after 6 years?

Answer: Rs. 4137
Explanation:
SI = ( Principal * Time * Rate ) / 100
= ( 9850 * 7 * 6 ) / 100
= Rs. 4137.


7. Consider a sum of money at simple interest amounts to Rs. 955 in 4 years and to Rs. 1055 in 5 years. The sum is?

Answer: 555
Explanation:
Simple Interest for 1 year = Rs. ( 1055 - 955 )
= Rs. 100
Simple Interest for 5 year = Rs. ( 100 * 5 )
= Rs. 500
Principal = Rs. ( 1055 - 500 )
= Rs. 555.


8. Anusha deposits an amount of Rs. 65800 to obtain a simple interest at the rate of 14% per annum for 4 year. What total amount will Anusha get at the end of 4 year?

Answer: Rs. 102648
Explanation:
Given data
P = 65,800/-, R = 14%, T = 4yr
Simple Interest = ( 65800 * 14 * 4 ) / 100
= 36848
∴ Amount = P + SI
⇒ 65800 + 36848
= Rs. 102648.

9. Ms. Sanjana deposits an amount of Rs. 41700 to obtain a simple interest at the rate of 12 p.c.per annum for 6 years. What total amount will Ms. Sanjana get at the end of 6 years?

Answer: Rs. 71724
Explanation:
Simple Interest = ( Principal * Time * Rate ) / 100
= ( 41700 * 12 * 6 ) / 100
= Rs. 30024
Amount received by Sanjana = Rs. ( 41700 + 30024 )
= Rs. 71724


10. Manish borrowed some money at the rate of 6% p.a. for the first two years, at the rate of 9% p.a. for the next three years, and at the rate of 14% p.a. for the rest of the period. If he pays a total interest of Rs. 11,400 at the end of nine years how much money did he borrow?

Answer: 12000
Explanation:
Let the sum borrowed be x.
[ ( x * 6 * 2 ) / 100 ] + [ ( x * 9 * 3 ) / 100 ] + [ ( x * 14 * 4 ) / 100 ] = 11400
( 3x / 25 ) + ( 27x / 100 ) + ( 14x / 25 ) = 11400
95x / 100 = 11400
x = ( 11400 * 100 ) / 95
= 12000.

Simple Interest concept

Simple Interest

Interest is defined as money charged for borrowing the money from someone / banks. There are four words mainly used in this category.

1. Principal

It is denoted by P (Principal ). Principal is the amount of money borrowed for a certain time.

2. Rate of interest

It is denoted by R ( Rate of interest ). Money paid for Rs. 100 per year called rate of interest.

3. Amount

It is denoted by A ( Amount ). The sum of Principal and interest is called amount.

4. Time

Denoted by T ( Time ). It is the period for which we borrowed money is called Time.

5. Simple Interest

Simple interest is denoted by SI. If the interest is calculated on the amount which we borrowed at any rate of interest for any period of time is called simple interest.

Basic Formulas

Simple Interest = ( Principal * Time * Rate ) / 100

Example sum

1. Find the simple interest on Rs. 68000 at [ 16 * ( 2 / 3 ) ] % per annum for 9 months?

Answer: Principal = Rs. 68000
Rate = ( 50 / 3 ) %
Time = ( 9 / 12 ) years
= ( 3 / 4 ) years
Simple interest = ( Principal * Rate * Time ) / 100
= Rs. [ ( 68000 * ( 50 / 3 ) * ( 3 / 4 ) ) / 100 ]
= Rs. [ ( 68000 * 50 * 3 ) / ( 50 * 4 * 100 ) ]
= Rs. 8500

Basic Formulas

Amount = Principal + Simple Interest

Example sum

1. Rs. 800 amounts to Rs. 920 in 3 years at simple interest. If the interest rate is increased by 3%, it would amount to how much ?

Answer: Principal = 800
Simple interest = 120
Time = 3 year
Rate = ( 100 * Simple interest ) / ( Principal * Time )
= ( 100 * 120 ) / ( 800 * 3 )
= 5%
New rate = 8 %
Principal = 800
Time = 3 year
Simple Interest = ( Principal * Rate * Time ) / 100
= ( 800 * 8 * 3 / 100 )
= 192
New Amount = Principal + Simple Interest New amoun = 800 + 192
= Rs. 992

Basic Formulas

Principal = ( 100 * Simple Interest ) / ( Time * Rate )

Example sum

1. A man took loan from a bank at the rate of 8% per annum. simple interest. After 4 years he had to pay Rs. 6200 interest only for the period. Find the principal amount borrowed by him ?

Answer: Time = 4 years
Simple Interest = Rs. 6200
Rate = 8%
Principal = ( 100 * Simple Interest ) / ( Rate * Time )
= ( 100 * 6200 ) / ( 8 * 4 )
= Rs. 19375

Basic Formulas

Time = ( 100 * Simple Interest ) / ( Principal * Rate )

Example sum

1. How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?

Answer: Simple interest = Rs. 81
Rate = 4.5 %
Principal = Rs. 450
Time = ( 100 * Simple Interest ) / ( Principal * Rate )
= ( 100 * 81) / ( 450 * 4.5 )
= 4 years

Basic Formulas

Rate = (100 * Simple Interest ) / ( Principal * Time )

Example sum

1. A four years NSC certificate was purchased for Rs. 500 with Rs. 1000 being the maturity value. Find the rate of Simple interest?

Answer: Principal = Rs. 500
Simple Interest = Rs. 500
Time = 4 years
Rate = ( 100 * Simple Interest ) / ( Principal * Time )
= (100 * 500 ) / ( 500 * 4 )
= 100 / 4
= 25%

Train solved Problems

Problems on Trains

1.  A train 100m long is running at the speed of 30 km/hr. Find the time taken by it to pass a man standing near the railway line?

Answer: 12 sec
Explanation:
Speed of the train = [ 30 * ( 5 / 18 ) ] m/sec [ ∴ ( a ) km/hr = ( a * ( 5 / 18 ) ) m/s ]
= ( 25 / 3 ) m/sec
Distance moved in passing the standing man = 100m
Required time taken = [ 100 / ( 25 / 3 ) ]
= [ 100 * ( 3 / 15 ) ]
= 12 sec.


2.  A train 150m long is running with a speed of 68kmph. In what time will it pass a man who is running at 8 kmph in the same direction in which the train is going?

Answer: 9 sec
Explanation:
Speed of the train relative to man = ( 68 - 8 )kmph
= 60 kmph
= [ 60 * ( 5 / 18 ) ] m/sec [ ∴ ( a ) km/hr = ( a * ( 5 / 18 ) ) ]
= [ ( 10 * 5 ) / 3 ]
= ( 50 / 3 )
Time taken by the train to cross the man = Time taken by it to cover 150 m at ( 50 / 3 ) m/sec
= [ ( 150 * 3 ) / 50 ]sec
= ( 3 * 3 )
= 9 sec.


3.  A 180m long train is running at 72 Kmph. If it crossed the platform in 20sec. then find the platform Length?

Answer: 220 m
Explanation:
Length = Speed * Time
Length = 72 km/hr * Time
Length = [ 72 * ( 5 / 18 ) ] * 20 [ ∴ ( x ) km/hr = ( x * ( 5 / 18 ) ) ]
= 20 * 20
Length = 400 m
Length of Platform = Length - Length of the Train
Length of Platform = 400 - 180
Length of Platform = 220 m.


4.  A train 137 metres and 163 metres in length are running towards each other on parallel lines, one at the rate of 42 kmph and another at 48 kmph. In what time will they be clear of each other from the moment they meet?

Answer: 12 seconds
Explanation:
Relative speeed of the trains = ( 42 + 48 ) kmph
= 90 kmph
= [ 90 * ( 5 / 18 ) ] m/sec
= 25 m/sec
Time taken by the trains to pass each other = ( 137 + 163 ) / 25
= 300 / 25
= 12 seconds.


5.  Two trains are running at 60 Kmph and 42 Kmph respectively, in same direction. Fast train completely passes a man sitting in the slower train in 30sec. What is the length of the faster train?

Answer: 150 m
Explanation:
Speed of the train = ( 60 - 42 ) Kmph ( ∴ Same direction Speed = first train - second train )
= 18 Kmph
Length = Speed * Time
Length = [ ( 18 * ( 5 / 18 ) ) * 30 ] m [ ∴ ( x ) kmph = ( x * ( 5 / 18 ) ) m/sec ]
= ( 5 * 30 ) m
= 150 m.


6.  A train 100 metres long takes 6 seconds to cross a man walking at 5 kmph in a direction opposite to that of the train. Find the speed of the train?

Answer: 55 kmph
Explanation:
Speed of the train relative to man = ( x + 5 ) kmph
= [ ( x + 5 ) * ( 5 / 18 ) ] m/sec
= [ ( 5x + 25 ) / 18 ] m/sec
⇒ 100 / [ ( x + 5 ) * ( 5 / 18 ) ] = 6
⇒ 100 * 18 / 5x + 25 = 6
1800 = 6 * ( 5x + 25 )
1800 = 30x + 150
3x = 1650
x = 1650 / 3
x = 55
Speed of the train 55 kmph.


7.  A train covers a distance of 12 km in 10 minutes. If it takes 6 seconds to pass a telegraph post, Find the length of the train?

Answer: 120 m
Explanation:
Speed = [ 12 / ( 10 / 60 ) ] km/hr ( ∴ 1 hr = 60 min )
Speed = [ ( 12 * 60 ) / 10 ] km/hr
= 72 km/hr
= [ 72 * ( 5 / 18 ) ] m/sec
= ( 4 * 5 ) m/sec
= 20 m/sec
Length of the train = ( speed * time )
= ( 20 * 6 ) m
= 120 m.


8.  The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 km in 4 hours, then find the speed of the first train?

Answer: 87.5 km/hr
Explanation:
Let the speed of two trains be 7x and 8x km/hr
8x = ( 400 / 4 )
8x = 100
x = 100 / 8
x = 12.5
Speed of first train = ( 7 * 12.5 ) km/hr
= 87.5 km/hr.


9.  A man sitting in a train which is traveling at 50 kmph observes that a goods train, traveling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed?

Answer: 62 kmph
Explanation:
Relative speed = ( 280 / 9 ) m/sec
= ( 280 / 9 ) * ( 18 / 5 ) kmph
= 56 * 2
= 112 kmph
Speed of goods train = ( 112 - 50 ) kmph
= 62 kmph.


10.  320m long train is running at 72 Kmph. How much time it will take to cross a platform of 180m long?

Answer: 25 Sec
Explanation:
Total Length = Platform Length + Train Length
Total Length = 320 m + 180 m
= 500 m
Distance = Speed * Time
500 = 72 * Time
500 = 72 * ( 5 / 18 ) * Time
Time = 25 Sec. 

Train concept

Problems On Trains 

Problems on trains and Time and Distance are almost same. The only difference is we have to consider the length of the train while solving problems on trains.

Properties of Proplems on Trains

1. Time taken by a train x meters long in passing a signal post or a pole or a standing man = Time taken by the train to cover x meters.

2. Time taken by a train x meters long in passing a stationary object of length y meters = Time taken by the train to cover ( x + y ) metres.

3. Suppose two trains or two bodies are moving in the same direction at u kmph andv kmph such that u > v, then their relative speed = ( u - v ) kmph.

4. If two trains of length x km and y km are moving in the same direction at u kmph and v kmph, where u > v, then time taken by faster train to cross the slower train = { ( x + y ) / ( u - v ) }hrs.

5. Suppose two trains or two bodies are moving in opposite directions at u kmphand v kmph. Then, their relative speed = ( u + v ) kmph.

6. If two trains of length x km and y km are moving in opposite directions at u kmphand v kmph, then: time taken by the trains to cross each other = ( x + y ) / ( u + v ) hrs.

7. If two trains start at the same time from two points A and B towards each other and after crossing they take a and b hours in reaching B and A respectively. Then, A′s speed : B′s; speed = [ ( 1 / b ) : ( 1 / a ) ].

Basic Formulas

x kmph = [ ( x * ( 5 / 18 ) ] m/sec.

Example sum

1. A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
Speed = [ 60 * ( 5 / 18 ) ] m/sec
= ( 50 / 3 ) m/sec
Length of the train = ( Speed * Time )
= [ ( 50 / 3 ) * 9 ] m
= 150 m

Basic Formulas

y m/sec = [ y * ( 18 / 5 ) ] km/hr

Example sum

1.  A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. Find the speed of the train?

Answer: Speed of the train relative to man = ( 125 / 10 ) m/sec
= ( 25 / 2 ) m/sec
= [ ( 25 / 2 ) * ( 18 / 5 ) ] km/hr
= 45 km/hr
Let the speed of the train be x km/hr.
Relative speed = ( x - 5 ) km/hr.
⇒ ( x - 5 ) = 45
⇒ x = 45 + 5
⇒ x = 50 km/hr

Basic Formulas

If two trains of p meters and q meters are moving in same direction at the speed of x m/s and y m/s ( x > y ) respectively then time taken by the faster train to overtake slower train is given by = [ ( p + q ) / ( x - y ) ]

Example sum

1.  Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. Find the length of each train?

Answer: Let the length of each train be x metres.
Distance covered = 2x metres.
Relative speed = ( 46 - 36 ) km/hr
= [ 10 * ( 5 / 18 ) ] m/sec
= ( 25 / 9 ) m/sec
⇒ ( 2x / 36 ) = ( 25 / 9 )
⇒ 2x = 100
x = 50

Basic Formulas

If two trains of p meters and q meters are moving in opposite direction at the speed of x m/s and y m/s respectively then time taken by trains to cross each other is given by = [ ( p + q ) / ( x + y ) ]

Example sum

1. Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?

Answer: Speed of the first train = ( 120 / 10 ) m/sec
= 12 m/sec
Speed of the second train = ( 120 / 15 ) m/sec
= 8 m/sec
Relative speed = ( 12 + 8 )
= 20 m/sec
Required time = [ ( 120 + 120 ) / 20 ] sec
= 12 sec.

Coding Decoding problems

Coding and Decoding

1.  If FRIEND isCoding and Decoding
coded as HUMJTK, how can CANDLE be written in that code?

Answer : EDRIRL
Explanation :
In the code, the first letter moves two letter forward.
The second letter is three letter forward, third letter is the four letter forwarded and so on after the corresponding letter in the word.

2.  If in a certain language, GAMBLE is coded as FBLCKF, how is GROUND coded in that code?

Answer : FSNVME
Explanation :
The first, third and fifth letters are each moved one step backward to obtain the code.
The second, fourth and sixth letters are each moved one step forward to obtain the corresponding letters of the code.

3 .  In as a certain code, 15789 is written as EGKPT and 2346 is written ALUR. How is 23549 written in that code?

Answer : ALGUT
Explanation :
In the given codes, the numbers are coded 2 as A, 3 as L, 5 as G, 4 as U and 9 as T.
So, 23549 is coded as ALGUT.

4.  If COOL is coded as DQRP, then write the code for HOT

Answer: IQW
Explanation:
In COOL, first letter is increased by 1, second by 2, third by 3 and so on.
So HOT will be coded as,
H + 1 = I
O + 2 = Q
T + 3 = W
So it will be IQW.

5.  If POLITICS is coded as OPILITSC, how will ARTICLES be coded in that language?

Answer: RAITLCSE
Explanation:
The positions of first and second, third and fourth, fifth and sixth letters are exchanged.

6.  If Z = 52 and ACT = 48, then BAT will be equal to the code?

Ans: 46
Explanation :
In the given code, A = 2, B = 4, C = 6,.... , Z = 52.
i.e. the position of english alphabets are incremented by 2.
So, ACT = 2 + 6 + 40 = 48
BAT = 4 + 2 + 40 = 46.

7.  In a certain code SCRIPT is written as TCQIQT. How is DIGEST written in that code?

Ans: EIFETT
Explanation :
In the code, the first and fifth letters are moved one step forward in the alphabet series while third letter is moved one step backward.
The other letters remain unchanged.
Hence DIGEST = EIFETT.

8.  If the first and the second letters in the word INORDINATE were interchanged also the third and the fourth letters, the fifth and the sixth letters and so on, which letters would be the eighth counting right to left? 

Answer : R
Explanation :
After implementing the given interchanges in the word INORDINATE it will become NIROIDANET.
Hence, the eighth letter from right to left is R.

9.  According to a military code, SYSTEM is SYSMET and NEARER is AENRER. What is the code for FRACTION ?

Ans: CARFNOIT
Explanation :
The letters of the first half and the letters of the second half of the word are separately reversed to obtain the code.

10.  If in a certan language FASHION is coded as FOIHSAN, how is PROBLEM coded in that code?

Ans: PELBORM
Explanation :
The first and the last letters of the word remain as such and the remaining letters are written in a reverse order, to obtain the code.

Coding Decoding concept

CODING - DECODING

A code is a system of signals. Therefore, coding  is a method of transmitting messages between the sender and receiver without a third person understanding it.The Coding and Decoding test is set up to judge the candidate's ability to decipher the law that codes a particular message and break the code to reveal the message. Following Table will help you code-decode -

A-1
B-2
C-3
D-4
E-5
F-6
G-7
H-8
I-9
J-10
K-11
L-12
M-13
N-14
O-15
P-16
Q-17
R-18
S-19
T-20
U-21
V-22
W-23
X-24
Y-25
Z-26
Z-1
Y-2
X-3
W-4
V-5
U-6
T-7
S-8
R-9
Q-10
P-11
O-12
N-13
M-14
L-15
K-16
J-17
I-18
H-19
G-20
F-21
E-22
D-23
C-24
B-25
A-26

A.  LETTER CODING -

A particular letter stands for another letter in letter coding.

Example - If COURSE is coded as FRXUVH, how is RACE coded in that code?
 

(1) HFDU (2) UCFH (3) UDFH (4) UDHF (5) UDFG

In the given code, each letter is moved three steps forward than the corresponding letter in the word. So R is coded as U, A as D, C as F, E as H. Hence (3) is the answer.

B.  NUMBER CODING -

In these questions, either numerical code values are assigned to a word or alphabetical code values are assigned to numbers. The candidate is required to analyse the code as per directions.

Case I: When numerical values are assigned to words.

Example : If  in a certain code ROPE is coded as 6821, CHAIR is coded as 73456 what will be the code for CRAPE?

(1) 73456   (2) 76421   (3) 77246    (4) 77123  (5) None of these

Clearly, in the given code, the alphabets are coded as follows.

R-6
O-8
P-2
E-1
C-7
H-3
A-4
I-5
R-6

So CRAPE is coded as 76421, So the answer is (2)

Case II: When alphabetical code values are assigned to the numbers.
Example: In a certain code 3456 is coded as ROPE. 15546 is coded as APPLE. Then how is 54613 coded?

(1) RPPEO   (2) ROPEA   (3) POEAR   (4) PAREO   (5) None of these
Clearly in the given figures, the numbers are coded as follows.

3-R
4-O
5-P
6-E
1-A
4-L
So 54613 is coded as POEAR. The answer is (3)

C.  MIXED CODING -
 

In this type of question, three or four complete messages are given in the coded language and the code for a particular word is asked. To analyse such codes, any two messages bearing the common word are picked up. The common code word will mean that word. Proceeding similarly by picking up all possible combinations of two messages the entire message can be analysed.

 
Example : If tee see pee means drink fruit juice, see kee lee means juice is sweet, and lee ree mee means he is intelligent, which word in that language means sweet?
(1) see (2) kee (3) lee (4) pee (5) tee
 

In the first and the second statements the common word is juice and the common code word is see. So see means juice. In the second and the third statements, the common word is ' is ' and the common code is lee. So lee means is. Thus in the second statement, the remaining word sweet is coded as kee. Hence the answer is (2).

D.   MIXED NUMBER CODING -

In this type of questions, three or four complete messages are given in the coded language and the code number for a particular word is asked.

Example: If  in a certain code language, 851 means good  sweet fruit; 783 means good red rose and 341 means rose and fruit which of the following digits stands for sweet in that language?

(1) 8       (2) 5        (3) 1         (4) 3            (5) None of these

In the first and the second statements, the common code digit is 8 and the common word is good. So 8 stands for good. In the first and the third statements, the common code digit is 1 and the common word is fruit. So 1 stands for fruit. Therefore in the first statement, 5 stands for sweet. Hence the answer is (2).

E.  DECODING -

In these questions, artificial or code values are assigned to a word or a group of words and the candidate is required to find out the original words.

 
Example : If in a certain language FLOWER is written as EKNVDQ, what will be written as GNTRD?

(1) HEOUS (2) HOUES (3) HUOSE (4) HOUSE (5) None of these

Each letter of the word is one step ahead of the corresponding letter of the code.

E-F
K-L
N-O
V-W
D-E
Q-R

G-H
N-O
T-U
R-S
D-E

Thus HOUSE is written as GNTRD, So the answer is (4)

F.  NEW TYPE OF CODING -

This is a kind of coding recently included in the Reasoning section. In this type of questions either alphabetical code values are assigned to symbols or symbols are assigned to alphabets. The candidate is required to analyse the code  as per direction.

 
Example. In a certain code ' TOME ' is written as @ $ * ? and ARE is written as  • £ ?   How can ' REMOTE ' be written in that code?

(1) £ ? • $ @ ?          (2) @ ? * $ @ ?          (3) £ ? * $ @ ?          (4) Cannot be determined        (5) None of these

Sol: From the data we have
T  = @    O = $    M = *   E = ?   and    A = •   R = £   E = ?

Hence REMOTE is coded as   £ ? * $ @ ?     So (3) is the answer.

Solved Problems On Number Series

Solved Problems 

1.  Look at this series: 14, 28, 20, 40, 32, 64,....
What number should come next?

Answer : 56
Explanation :
This is an alternating multiplication and subtracting series: First, multiply by 2 and then subtract 8.


2 . Look at this series: 4, 7, 25, 10, __, 20, 16, 19
What number should fill the blank?

Answer : 13
Explanation :
Two series alternate here, with every third number following a different pattern.
In the first series(odd position value), 3 is added to each number to arrive at the next.
In the second series(even position value), 5 is subtracted from each number to arrive at the next.


3. Look at the series and find the pair numbers.
10 20 25 35 40 50 55 ? ?

Answer : 65 70
Explanation :
This is an alternating addition series.
In which 10 is added, then 5, then 10, and so on.


4 . Look at this series: 664, 332, 340, 170, __, 89
What number should fill the blank?

Answer : 178
Explanation :
This is an alternating division and addition series.
The number is divide by 2, and then add 8.


5. Look at the series 72, 76, 73, 77, 74, __, 75
What number should fill the blank?

Answer : 78
Explanation :
This is an alternating addition subtraction series.
In which addition of 4 and the subtraction of 3.

6.  Look at this series and find the pair numbers.
6 20 8 14 10 8 12 ....

Answer : 2 14
Explanation :
This is an alternating addition and subtraction series.
In the first pattern, 2 is added to each number to arrive at the next.
In the alternate pattern, 6 is subtracted from each number to arrive at the next.


7.  Look at the series 201, 202, 204, 207, __
What number should come next?

Answer : 211
Explanation :
In this addition series, 1 is added to the first number.
The number 2 is added to the second number; 3 is added to the third number.
The number 4 is added to the fourth number; and go on.

8. Look at this series and find the pair numbers.
21 25 18 29 33 18......

Answer : 37 41
Explanation :
This is a simple addition series with a random number, 18, interpolated as every third number.
In the series, 4 is added to each number except 18, to arrive at the next number.


9. Look at this series and find the pair numbers.
61 57 50 61 43 36 61.....

Answer : 29 22
Explanation :
This is an alternating repetition series.
In which a random number, 61, is interpolated as every third number into an otherwise simple subtraction series.
Starting with the second number, 57, each number (except 61) is 7 less than the previous number.


10. Look at this series: 83, 73, 93, 63, __, 93, 43
What number should fill the blank?

Answer : 53
Explanation :
This is a simple subtraction series.
In which a random number, 93, is interpolated as every third number.
In the subtraction series, 10 is subtracted from each number to arrive at the next.


11.  Look at this series: 2, 3, 5, 7, 11, ?, 17
What number should fill the blank?

Answer : 13
Explanation :
The given series consists of prime numbers starting from 2.
The prime number after 11 is 13.
So, 13 is the missing number.


12. L ook at this series and find the pair numbers.
8 22 12 16 22 20 24 ....

Answer : 22 28
Explanation :
This is an alternating repetition series, with a random number, 22, interpolated as every third number into an otherwise simple addition series.
In the addition series, 4 is added to each number to arrive at the next number.


13. Look at this16. Look at this series: 14, 28, 20, 40, 32, 64,.... 
What number should come next? 
Answer : 56
Explanation :
This is an alternating multiplication and subtracting series: First, multiply by 2 and then subtract 8



14.  Look at this series and find the pair numbers.
18 21 25 18 29 33 18....

Answer : 37 41
Explanation :
This is a simple addition series with a random number, 18, interpolated as every third number.
In the series, 4 is added to each number except 18, to arrive at the next number.


15.  Look at this series 1, 6, 13, 22, 33,..... What number should fill the blank?

Answer : 46
Explanation :
This is a simple addition series. The pattern is + 5, + 7, + 9, + 11,...
Missing number = 33 + 13 = 46.

Letter Series Completion problem

Letter Series Completion

1.  In these series, you will be looking the letter pattern. Fill the blank in the middle of the series.
QPO, NML, KJI, _____, EDC

Answer : HGF
Explanation :
This series consists of letters in a reverse alphabetical order.


2.  In these series, you will be looking at both the letter pattern. Fill the blank in the end of the series.
JE, LH, OL, SQ, ----

Answer : XW
Explanation :
The first letter moves 2, 3, 4 ... steps forward to obtain the code.
The second letter moves 3, 4, 5 ... steps forward to obtain the corresponding letters of the code.


3.  Find the missing letter in the given series:
Y, B, T, G, O, ?

Answer: L
Explanation:
The given sequence is a combination of two series :
I. Y, T, O and II. B, G, ?
I consists of 2nd, 7th and 12th letters from the end of the English alphabet, while
II consists of 2nd, 7th and 12th letters from the beginning of the English alphabet.
So, the missing letter in II is the 12th letter from the beginning of the English alphabet, which is L.


4.  Find the missing letter in the series:
QIOK : MMKO :: YAWC : ?

Answer: UESG
Explanation:
The 1st and 3rd letters in the element QIOK is moved four steps backward and the 2nd and 4th letters in the same element is moved four steps forward to obtain MMKO
Similarly, for the questioned element YAWC, Y and W is moved 4 steps backward to give U and S
and the letters A and C is moved 4 steps forward to give E and G.
Hence, the answer is UESG.


5.  Fill the blank in the end of the series. 
JE, LH, OL, SQ,.....? 

Answer : XW
Explanation :
The first letter(J,L,O,S) moves 2, 3, 4, 5, ... steps forward.
The second letter(E,H,L,Q) moves 3, 4, 5, 6, ..... steps forward in this series.


6.  In these series, you will be looking at the letter pattern. Fill the blank in the middle of the series.
FAG GAF HAI IAH _____

Answer : JAK
Explanation :
The middle letters are static,so concentrate on the first and third letters.
The series involves an alphabetical order with a reversal of the letters.
The first letters are in alphabetical order: F, G, H, I, J. The second and fourth segments are reversals of the first and third segments.


7.  In these series, you will be looking at both the letter pattern. Fill the blank in the end of the series.
DKY,FJW,HIU,JHS,_____

Answer : LGQ
Explanation :
The first letter of moves two steps forward to obtain the first letter.
The second letter of moves one step backward to obtain the second letter of the successive term.
The third letter moves two steps backward to obtain the third letter of the subsequent term.


8.  Look at this series: J14, L16, __, P20, R22. 
What number should come next? 

Answer : N18
Explanation :
In this series, the letters moves two steps forward.
The number is increase by 2.


9.  In these series, you will be looking at both the letter pattern. Fill the blank in the end of the series.
JAK KBL LCM MDN ____

Answer : NEO
Explanation :
This is an alternating series in alphabetical order.
The middle letters follow the order ABCDE. The first and third letters are alphabetical beginning with J.
The third letter is repeated as a first letter in each subsequent three-letter segment.


10.  Look at this series: U32, V29, __, X23, Y20, . . .. 
What number should fill the blank? 

Answer : W26
Explanation :
In this series, the letters progress by 1.
The numbers decrease by 3.