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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