Problems On Chain Rule

Solved Problems 

1.  If 36 men can do a piece of work in 25 hours, in how many hours will 15 men do it?

Answer: 60 hours
Explanation:
Let the required number of hours be x.
Less men, More hours (∴ Indirect proportion )
⇒ 15 : 36 :: 25 : x
⇒ 15 * x = 36 * 25
x = ( 36 * 25 ) / 15
= 60 hours
Hence 15 men can do it in 60 hours.


2.  If the wages of 6 men for 15 days be Rs. 2100, then find the wages of 9 men for 12 days?

Answer: Rs. 2520
Explanation:
Let the required wages be x.
⇒ More men, More wages. ( ∴ Direct proportion )
⇒ Less days, Less wages. ( ∴ Direct proportion )
Men = 6 : 9 :: 2100 : x
Days = 15 : 12 :: 2100 : x
⇒ ( 6 * 15 * x ) = ( 9 * 12 * 2100 )
x = [ ( 9 * 12 * 2100 ) / ( 6 * 15 ) ]
x = 420 * 6
x = 2520
Hence, the required wages are Rs. 2520.


3.  8 children and 12 men complete a certain piece of work in 9 days. If each child takes twice the time taken by a man to finish the work, in how many days will 12 men finish the same work?

Answer: 12 days
Explanation:
2 children = 1 man
⇒ ( 8 children + 12 men ) = 16 men
⇒ Less men, More days ( ∴ Indirect proportion )
⇒ 12 : 16 :: 9 : x
12x = ( 16 * 9 )
12x = 144
x = 144 / 12
x = 12 days.


4.  Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?

Answer: 1800
Explanation:
Let the required number of bottles be x.
⇒ More machines, More bottles ( ∴ Direct Proportion )
⇒ More minutes, More bottles ( ∴ Direct Proportion )
Machines = 6 : 10 :: 270 : x
Time (in minutes) = 1 : 4 :: 270 : x
⇒ 6 * 1 * x = 10 * 4 * 270
x = ( 10 * 4 * 270 ) / ( 6 * 1 )
= 20 * 90
x = 1800.


5.  4 mat weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat weavers in 8 days?

Answer: 16
Explanation:
Let the required number of mats be x.
⇒ More mat weavers, more mats ( ∴ Direct proportion )
⇒ More days, more mats ( ∴ Direct proportion )
Mat weavers = 4 : 8 :: 4 : x
Days = 4 : 8 :: 4 : x
⇒ 4 * 4 * x = 8 * 8 * 4
x = ( 8 * 8 * 4 ) / ( 4 * 4 )
x = 2 * 2 * 4
x = 16.


6.  If a quarter kg of potato costs 60 paise, how many paise will 200 gm cost?

Answer: 48
Explanation:
Let the required weight be x kg.
⇒ Less weight, Less cost ( ∴ Direct Proportion )
⇒ 250 : 200 :: 60 : x
⇒ 250 * x = ( 200 * 60 )
x = ( 200 * 60 ) / 250
x = 8 * 6
x = 48.


7.  In a hospital there is a consumption of 1350 litres of milk for 70 patients for 30 days. How many patients will consume 1710 litres of milk in 28 days?

Answer: 95 patients
Explanation:
Let the required number of number be x.
⇒ More litres, more patients ( ∴ Direct proportion )
⇒ Less days, more patients ( ∴ Indirect proportion )
Litres = 1350 : 1710 :: 70 : x
Days = 20 : 8 :: 70 : x
⇒ x = ( 1710 * 30 * 70 ) / ( 1350 * 28 )
= 19 * 5
= 95 patients.


8.  39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?

Answer: 13 days
Explanation:
Let the required number of days be x.
⇒ Less persons, More days ( ∴ Indirect Proportion )
⇒ More working hours per day, Less days ( ∴ Indirect Proportion )
Persons = 30 : 39 :: 12 : x
Working hours/day = 6 : 5 :: 12 : x
⇒ ( 30 * 6 * x ) = ( 39 * 5 * 12 )
x = ( 39 * 5 * 12 ) / ( 30 * 6 )
x = 13 days.

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