Aptitude - Chain Rule
6.
A tree 6m tall casts a 4m long shadow. At the same time, a flagpole casts a 50m long shadow. How long is the flagpole ?
Answer
Let the length of the flagpole be x metres.
Longer is the shadow, longer is the object (Direct)
4 : 50 :: 6 : x ⇒ 4x = (50 x 6)
⇒ x = (50 x 6)4 = 75m
Length of flagpole = 75m
Answer :
Option BExplanation :
Let the length of the flagpole be x metres.
Longer is the shadow, longer is the object (Direct)
4 : 50 :: 6 : x ⇒ 4x = (50 x 6)
⇒ x = (50 x 6)4 = 75m
Length of flagpole = 75m
7.
8 men can finish a piece of work in 40 days. If 2 more men join with them, then the work will be completed in
Answer
Let 10 men finish it in x days.
More men, less days (Indirect)
10 : 8 :: 40 : x ⇒ 10x = 8 x 40
⇒ x = 8 x 4010 = 32 days
Answer :
Option BExplanation :
Let 10 men finish it in x days.
More men, less days (Indirect)
10 : 8 :: 40 : x ⇒ 10x = 8 x 40
⇒ x = 8 x 4010 = 32 days
8.
If 3 persons weave 336 shawls in 14 days, how many shawls will 8 persons weave in 5 days ?
Answer
Let the required number of shawls be x
More persons, more shawls (Direct)
Less days, less shawls (Direct)
Persons 3 : 8Days 14 : 5
:: 336 : x
∴ 3 x 14 x x = (8 x 5 x 336) ⇒ x = 8 x 5 x 3363 x 14 = 320 shawls
Answer :
Option DExplanation :
Let the required number of shawls be x
More persons, more shawls (Direct)
Less days, less shawls (Direct)
Persons 3 : 8Days 14 : 5
:: 336 : x∴ 3 x 14 x x = (8 x 5 x 336) ⇒ x = 8 x 5 x 3363 x 14 = 320 shawls
9.
If 5 spiders can catch 5 flies in 5 minutes, how many flies can 100 spiders catch in 100 minutes ?
Answer
Let the required number of flies be x
More spiders, more flies (Direct)
More time, more flies (Direct)
Spiders 5 : 100Time 5 : 100 :: 5 : x
∴ 5 x 5 x x = (100 x 100 x 5) ⇒ x = 100 x 100 x 55 x 5 = 2000 flies
Answer :
Option DExplanation :
Let the required number of flies be x
More spiders, more flies (Direct)
More time, more flies (Direct)
Spiders 5 : 100Time 5 : 100
:: 5 : x∴ 5 x 5 x x = (100 x 100 x 5) ⇒ x = 100 x 100 x 55 x 5 = 2000 flies
10.
Four examiners can examine a certain number of answer papers in 10 days by working for 5 hours a day. For how many hours in a day would 2 examiners have to work in order to examine twice the number of answer papers in 20 days ?
Answer
Let the number of hours per day be x
More days, less hours per day (Indirect)
Less examiners, more hours per day (Indirect)
More answer papers, more hours per day (Direct)
Days 20 : 10 Examiners 2 : 4
Answer Papers 1 : 2
:: 5 : x
∴ (20 x 2 x 1 x x) = (10 x 4 x 2 x 5) ⇒ x = 400040= 10 hrs per day
Answer :
Option DExplanation :
Let the number of hours per day be x
More days, less hours per day (Indirect)
Less examiners, more hours per day (Indirect)
More answer papers, more hours per day (Direct)
Days 20 : 10 Examiners 2 : 4
Answer Papers 1 : 2
:: 5 : x∴ (20 x 2 x 1 x x) = (10 x 4 x 2 x 5) ⇒ x = 400040= 10 hrs per day
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