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A and B can complete a work in 15 days. A started the work and left after working for 4 days, then B completes the remaining work in 20 days. Find in how much time, A alone can complete the work?
1. 42
2. 45
3. 48
4. 40

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Correct Answer - Option 3 : 48

Given:

Time taken by (A + B) to complete the work = 15 days

No. of days worked by A alone = 4 days

No. of days worked by B alone = 20 days

Concept used:

Work done in both cases will be the same.

Formula used:

Total Work done = Efficiency × No. of days worked

Calculation:

Let the efficiency of A and B be a and b.

According to the question,

⇒ (a + b) × 15 = a × 4 + b × 20

⇒ 15a + 15b = 4a + 20b

⇒ 11a = 5b

⇒ a/b = 5/11

Now, total work done = (5 + 11) × 15

⇒ 16 × 15

⇒ 240

No of days required by A to finish the work = Total Work/Efficiency of A

⇒ 240/5

⇒ 48 days.

∴ The A alone can complete the work in 48 days.

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