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A can do a work in 21 days. B is 50% more efficient than A. C is twice efficient than B. A started the work alone and worked for some days and left the work then B and C joined together and finished the work in 2 days. In how many days does A worked alone?

A can do a work in 21 days. B is 50% more efficient than A. C is twice efficient than B. A started the work alone and worked for some days and left the work then B and C joined together and finished the work in 2 days. In how many days does A worked alone? Correct Answer 12

Given:

A can do a work in 21 days.

B is 50% more efficient than A.

C is twice efficient than B.

A started the work alone and worked for some days and left the work.

Then B and C joined together and finished the work in 2 days.

Formula Used:

If A and B can together finish a work in t days and alone can finish the work in a and b days respectively,

Then, 1/a + 1/b = 1/t

Work = Time × Efficiency

Calculation:

Time required by B = 2/3 × 21 = 14 days

C will take 7 days (As C is twice efficient than B)

Let total work be = LCM of 21, 14, 7 = 42 units and let A worked for x days alone.

Efficiency of A = 2

Efficiency of B = 3

Efficiency of A = 6

ATQ,

⇒ 2x + 9 × 2 = 42

⇒ 2x = 24

⇒ X = 12 days

∴ A works for 12 days alone.

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