A alone can complete a job in 12 days and B alone in 18 days. A and B agree to do the work for ₹7,200. With C's help they finish it in 5 days. How much should C be paid?
₹2,200
Wages are shared in proportion to the amount of work done by each person.
Step 1 – work done in 5 days:
A's work = \(\dfrac{5}{12}\), B's work = \(\dfrac{5}{18}\).
Together = \(\dfrac{5}{12} + \dfrac{5}{18} = \dfrac{15 + 10}{36} = \dfrac{25}{36}\).
So C's work = \(1 - \dfrac{25}{36} = \dfrac{11}{36}\).
Step 2 – ratio of wages A : B : C = 15 : 10 : 11 (out of 36 parts).
Step 3 – C's share:
\(\dfrac{11}{36} \times 7200 = ₹2200\)
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