1.

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 B2). Quantity A < Quantity B3). Quantity A ≥ Quantity B4). Quantity A ≤ Quantity B

Answer»

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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