Question 9

A can dig a trench in 12 days, B can dig it in 16 days and C can dig it in 18 days. If they dig the trench, working together and get a sum of Rs. 5800 for it, then share of A in the sum is

The money is shared in the ratio of their work rates $$\frac{1}{12} \colon \frac{1}{16} \colon \frac{1}{18}$$. Multiplying by 144 gives $$12 \colon 9 \colon 8$$, which adds up to 29. So A's share is $$\frac{12}{29} \times 5800 = 2400$$ rupees.

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