Question:

A can do a piece of work in 8 days and B alone can do the same work in 10 days. A and B agreed to do the work together for Rs. 720. With the help of C, they finished the work in 4 days. How much is C to be paid?

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When finding wages in joint work problems, distribute payment in proportion to work done by each person.
Updated On: Aug 14, 2025
  • Rs. 80
  • Rs. 70
  • Rs. 72
  • Rs. 82
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The Correct Option is C

Solution and Explanation

Work done by A in 1 day = \( \frac{1}{8} \) of the total work.
Work done by B in 1 day = \( \frac{1}{10} \) of the total work.
Together, in 1 day, A and B can complete: \[ \frac{1}{8} + \frac{1}{10} = \frac{5 + 4}{40} = \frac{9}{40} \] Work done by A and B in 4 days = \( 4 \times \frac{9}{40} = \frac{36}{40} \).
Thus, the remaining work done by C = \( 1 - \frac{36}{40} = \frac{4}{40} = \frac{1}{10} \) of the total work.
Since Rs. 720 is the total payment, C’s share is proportional to the work done.
C’s share = \( \frac{1}{10} \times 720 = 72 \) rupees.
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