The number of days in which A and B together can finish a piece of work is 12 days less than the time taken by A alone and 27 days less than the time taken by B alone to finish the work. If A and B completed the work in 15 days with the help of C and got a total compensation of Rs 3000 for the work, then what is the share of C?
Solution
Correct Answer: Option D
Let the number of days in which work has been completed by A and B is n then A takes (n + 12) days and B takes (n + 27) days to finish the work.
\(So,\ \ \ \frac{1}{{{\text{n}} + 12}}{\text{}} + {\text{}}\frac{1}{{{\text{n}} + {\text{}}27}}{\text{}} = {\text{}}\frac{1}{{\text{n}}},\)
⇒ n [(n + 12) + (n + 27)] = (n + 12) (n + 27)
⇒ 2n2 + 39n = n2 + 39n + 324
⇒ n2 = 324 ⇒ n = 18
So, if the total work is 1 unit then the work done by both A and B together in one day is 1/18 unit. So total work done by these two in 15 days = 15/18 = 5/6th of work
So the work done by C is = 1/6 th of the total work
So the money which C will get = \(\frac{1}{6} \times 3000 = {\text{Rs}}\ 500\)
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