Discussion

Question:

Two workers A and B working together completed a job in 5 days. If A worked twice as efficiently as he actually did and B worked 1/3^rd as efficiently as he actually did, the work would have completed in 3 days. Find time for B to complete the job alone.

Explanation:

Let them take A and B days respectively to complete the work alone.

∴ $\frac{1}{A} + \frac{1}{B} = \frac{1}{5}$ …(1)

Also, $\frac{1}{A ∕ 2} + \frac{1}{3 B} = \frac{1}{3}$

⇒ $\frac{2}{A} + \frac{1}{3 B} = \frac{1}{3}$ …(2)

(1) × 2 - (2), we get

$\frac{2}{B} - \frac{1}{3 B} = \frac{2}{5} - \frac{1}{3}$

∴ B = 25 days.

Hence, option (c).

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