Question : A and B undertake a piece of work for Rs. 250. A alone can do that work in 5 days and B alone can do that work in 15 days. With the help of C, they finish the work in 3 days. If everyone gets paid in proportion to the work done by them, the amount C will get is:
Option 1: Rs. 50
Option 2: Rs. 100
Option 3: Rs. 150
Option 4: Rs. 200
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Correct Answer: Rs. 50
Solution : Given: A and B undertake a piece of work for Rs. 250. A's 1 day's work = $\frac{1}{5}$ B's 1 day's work = $\frac{1}{15}$ (A + B + C)'s 1 day's work = $\frac{1}{3}$ So, C's 1 day's work = $\frac{1}{3}-(\frac{1}{5}+\frac{1}{15})=\frac{1}{3}-\frac{4}{15}=\frac{1}{15}$ The ratio of efficiencies by A, B, C is $\frac{1}{5}:\frac{1}{15}:\frac{1}{15}=3:1:1$ So, C's amount $=\frac{1}{3+1+1}×250=50$ Hence, the correct answer is Rs. 50.
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