Question:

A alone can finish a piece of work in 10 days which B alone can do in 15 days. If they work together and finish it, then out of total wages of Rs 3000, A will get

(a) Rs 1200

(b) Rs 1500

(c) Rs 1800

(d) Rs 2000

Solution:

(c) Rs 1800

Since the wage distribution will follow the work distribution ratio, we have:

Work done by $\mathrm{A}$ in 1 day $=\frac{1}{10}$

Work done by $B$ in 1 day $=\frac{1}{15}$

Net work done by $(\mathrm{A}+\mathrm{B})$ in 1 day $=\frac{1}{10}+\frac{1}{15}=\frac{5}{30}=\frac{1}{6}$

i.e., $(A+B)$ will take 6 days to complete the work.

A’s share of work in a day $=\frac{1}{10} \div \frac{1}{6}=\frac{1}{10} \times \frac{6}{1}=\frac{6}{10}=\frac{3}{5}$

$\therefore$ A’s wage $=\frac{3}{5} \times 3000=\mathrm{Rs} 1800$