Question : A alone can complete a work in 10 days. B alone can do the same work in 12 days, and C alone can do the same work in 15 days. They jointly complete the work and earn Rs. 4500. What is the share of C?
Option 1: Rs. 1800
Option 2: Rs. 900
Option 3: Rs. 1200
Option 4: Rs. 1500
Correct Answer: Rs. 1200
Solution : Total earnings = Rs. 4500 A alone can complete the work in = 10 days ∴ A’s 1 day’s work = $\frac{1}{10}$ B alone can complete the work in = 12 days ∴ B’s 1 day’s work = $\frac{1}{12}$ C alone can complete the work in = 15 days ∴ C’s 1 day’s work = $\frac{1}{15}$ ∴ Ratio of work of A, B and C = $\frac{1}{10}:\frac{1}{12}:\frac{1}{15}$ = $\frac{1}{10}×60:\frac{1}{12}×60:\frac{1}{15}×60$ = $6∶5∶4$ Total earnings = Rs. 4500 ∴ Share of C = 4500 × $\frac{4}{6+5+4}$ = 4500 × $\frac{4}{15}$ = Rs. 1200 Hence, the correct answer is Rs. 1200.
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