Given below are two quantities named A & B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers. Quantity A: Three persons P, Q and R working togethe

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Given below are two quantities named A & B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers. Quantity A: Three persons P, Q and R working togethe

Asked on 2019-05-01 14:58:16 by Guest | Votes 0 | Views: 111 | Tags: time and work | quantitative aptitude | Add Bounty

Given below are two quantities named A & B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers.

Quantity A: Three persons P, Q and R working together can complete a piece of work in 30 days. P & R together can finish the work in half the time Q can finish it and P & Q together are thrice efficient than R. In how many days Q can finish the work alone?

Quantity B: Two persons A and B can finish a piece of work in 12 days. If A works thrice its efficiency and B works half of its efficiency then the work will be finished in 8 days. Find the time in which A will complete thrice the work alone.
1). Quantity A > Quantity B
2). Quantity A < Quantity B
3). Quantity A ≥ Quantity B
4). Quantity A ≤ Quantity B

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Answered by Guest on 2019-05-25 19:35:33 | Votes 1 | #

Quantity A:

Suppose the efficiencies of P, Q and R is p, q and r respectively

Given that P & R together can finish the work in half the time Q can finish it

⇒ Efficiency of P & R together will be twice the efficiency of Q

⇒ (p + r) ? q = 2 ? 1 = 8 ? 4 (Let)

P & Q together are thrice efficient than R

⇒ (p + q) ? r = 3 ? 1 = 9 ? 3

⇒ p ? q ? r = 5 ? 4 ? 3

Since P, Q and R working together can complete the work in 30 days

⇒ Total units of work = 12 × 30 = 360 units

⇒ Time taken by Q to complete the work = 360/4 = 90 days

Quantity B:

Suppose the efficiencies of A and B are ‘a’ and ‘b’ respectively

According to the given statements :

⇒ 12(a + b) = 8(3a + b/2)

⇒ 12a + 12b = 24a + 4b

⇒ 12a = 8b

⇒ a ? b = 2 ? 3

Since A and B can finish the work in 12 days

⇒ Total units of work = 5× 12 = 60 units

⇒ Time taken by A to complete thrice the work = 3 × 60/2 = 90 days

∴ Quantity A = Quantity B

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