The efficiency of A, B, and C is 2 : 3 : 5. A alone can complete a work in 50 days. They all work together for 5 days and then C left the work, in how many days A and B together can complete the remaining work?

  1. 50 days
  2. 30 days
  3. 20 days
  4. 10 days

Answer (Detailed Solution Below)

Option 4 : 10 days
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Detailed Solution

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Given:

Efficiency of A, B and C = 2 : 3 : 5

A alone can complete the work in = 50 days

Formula:

Total work = Efficiency × Time

Calculation:

Let efficiency of A be 2 units/day

Efficiency of A, B and C = 2 : 3 : 5

Total work = 2 × 50 = 100 units

Work done by A, B and C in 5 days = (2 + 3 + 5) × 5 = 10 × 5 = 50 units

Remaining work = 100 – 50 = 50 units

∴ Time taken by A and B to complete the remaining work = 50/(2 + 3) = 50/5 = 10 days

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