Question

A and B can do a piece of work in 30 days, while B and C can do the same in 24 days; and C and A in 20 days. They all work together for 12 days until B and C leave. How many more days will it take for A to finish the work?
1. 8 days
2. 14 days
3. 12 days
4. 10 days

Answer 1

Correct Answer - Option 3 : 12 days

Given:

Time taken by A and B = 30 days

Time taken by B and C = 24 days

Time taken by C and A = 20 days

Formula used:

Total work = Efficiency × time

Calculation:

Total work = (LCM of 30, 24, and 20)

Total work = 120 units

The efficiency of (A + B) = 120/30 = 4 units/day     ...1)

The efficiency of (B + C) = 120/24 = 5 units/day     ...2)

The efficiency of (C + A) = 120/20 = 6 units/day     ...3)

From equations (1), (2) and (3), we get

A + B + B + C + C + A = 4 + 5 + 6

⇒ 2(A + B + C) = 15

⇒ (A + B + C) = 15/2 units/day     ...4)

From equations (2) and (4), we get

A + 5 = 15/2

⇒ A = 5/2 units/day

Total work done by (A + B + C) in 12 days = 12 × (15/2)

⇒ 90 units

Remaining work = 120 - 90 = 30 units

Time taken by A to complete the remaining work = Remaining work/Efficiency of A

⇒ 30/(5/2) = (30 × 2)/5

⇒ 12 days

∴ Time taken by A to complete the remaining work in 12 days.