Aptitude - Chain Rule
1.
6 dozen eggs are bought for Rs. 48. How much will 132 eggs cost ?
Answer
Let the required amouunt be Rs. x
More eggs, more cost (Direct)
72 : 132 :: 48 : x ⇒ 72x = 132 x 48
⇒ x = 132 x 4872 = 88
∴ Required amount = Rs. 88
Answer :
Option DExplanation :
Let the required amouunt be Rs. x
More eggs, more cost (Direct)
72 : 132 :: 48 : x ⇒ 72x = 132 x 48
⇒ x = 132 x 4872 = 88
∴ Required amount = Rs. 88
2.
A garrison of 500 men had provisions for 24 days. However a reinforcement of 300 men arrived. The food will now last for
Answer
Let the required number of days be x
More men, less days (Indirect)
800 : 500 :: 24 : x ⇒ 800x = 500 x 24
⇒ x = 500 x 24800 = 15
∴ The food will now last for 15 days
Answer :
Option DExplanation :
Let the required number of days be x
More men, less days (Indirect)
800 : 500 :: 24 : x ⇒ 800x = 500 x 24
⇒ x = 500 x 24800 = 15
∴ The food will now last for 15 days
3.
If 21 cows eat as much as 15 buffaloes, how many cows will eat as much as 35 buffaloes ?
Answer
15 buffaloes ≡ 21 cows ⇒ 1 buffalo ≡ 2115 cows = 75 cows
⇒ 35 buffaloes ≡ 35 x 75 cows = 49 cows
Answer :
Option AExplanation :
15 buffaloes ≡ 21 cows ⇒ 1 buffalo ≡ 2115 cows = 75 cows
⇒ 35 buffaloes ≡ 35 x 75 cows = 49 cows
4.
A does half as much work as B in one-sixth of time. If together they take 10 days to complete the work, how much time shall B alone take to do it ?
Answer
Suppose B takes x days to finish the work.
Then, A takes x6 days to finish half the work.
∴ A takes 2x6 = x3 days to finish the work.
1x + 3x = 110 ⇒ 4x = 110 ⇒ x = 40
Hence, B alone takes 40 days to finish the work.
Answer :
Option CExplanation :
Suppose B takes x days to finish the work.
Then, A takes x6 days to finish half the work.
∴ A takes 2x6 = x3 days to finish the work.
1x + 3x = 110 ⇒ 4x = 110 ⇒ x = 40
Hence, B alone takes 40 days to finish the work.
5.
Two persons can complete a piece of work in 9 days. How many more persons are required to complete double the work in 12 days ?
Answer
Let the required number of persons be x
More work, more persons (Direct)
More days, less persons (Indirect)
Work 1 : 2Days 12 : 9
:: 2 : (2 + x)
1 x 12 x (2 + x) = (2 x 9 x 2) ⇒ (2 + x) = 3612 = 3
⇒ (2 + x) = 3 ⇒ x = 1
Answer :
Option AExplanation :
Let the required number of persons be x
More work, more persons (Direct)
More days, less persons (Indirect)
Work 1 : 2Days 12 : 9
:: 2 : (2 + x)1 x 12 x (2 + x) = (2 x 9 x 2) ⇒ (2 + x) = 3612 = 3
⇒ (2 + x) = 3 ⇒ x = 1
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