Discussion

Question:

A can do a piece of work in 20 days and B alone can do it in 30 days. A and B undertook to do it for Rs. 600. With the help of C they finished it in 10 days. How much is paid to C?

Explanation:

Given, $\frac{1}{A} + \frac{1}{B} + \frac{1}{C} = \frac{1}{10}$

⇒ $\frac{1}{20} + \frac{1}{30} + \frac{1}{C} = \frac{1}{10}$

⇒ $\frac{1}{C} = \frac{1}{10} - \frac{1}{12} = \frac{1}{60}$

C alone will take 60 days.

Since all three work for same number of days, the payment will be divided in the ratio of their efficiencies.

Rs. 300 is divided in the ratio A : B : C = $\frac{1}{20} : \frac{1}{30} : \frac{1}{60}$ = 3 : 2 : 1.

∴ C gets = $\frac{1}{6}$ × 600 = 100.

Hence, option (d).

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