Question

A can do a piece of work in 12 days while B alone can do it in 15 days. With the help of C they can finish it in 5 days. If they are paid Rs.960 for the whole work. How much money A gets ?

Answer 1

Given: Time taken by A to complete the work = 12 days

Time taken by B to complete the work = 15 days

Time taken by A, B and C to complete the work together = 5 days

Calculation: A can do a piece of work in 12 days.

∴ Part of work done by A in 1 day = 1/12 B can do a piece of work in 15 days

∴ Part of work done by B in 1 day = 1/15 Let, C can do a piece of work in ‘x’ days ∴ Part of work done by C in 1 day = 1 / x

∵ A, B and C can do the work in 5 days 1A + 1B + 1C = 15 112 + 115 + 1x = 15 ⇒ (9/12) + (5 / x) = 1

⇒ 5 / x = 1 - (9/12) ⇒ 5 / x = 3/12

⇒ x = 20

∴ Part of work done by C in 1 day = 1/20 ∴ Ratio of part of work done by A, B and C. = 1/12: 1/15: 1/20

∵ LCM of 12, 15 and 20 is 60. = (1/12) × 60: (1/15) × 60: (1/20) × 60 = 5: 4: 3

∴ Ratio of money A, B and C get = 5: 4: 3 Given, Total money got by A, B and C together = Rs.960

∴ Money A gets = {5 / (5 + 4 + 3) × 960 = (5/12) × 960 = Rs.400

Money gets A 400 rupees