Anil and Karan together can do a work in 20 days. Karan and Himanshu together can do the same work in 25 days. Himanshu and Anil together can do the same work in 50 days. In how many days can Himanshu alone do the same work?
200 days
One-day work: A + K = \(\frac{1}{20}\), K + H = \(\frac{1}{25}\), H + A = \(\frac{1}{50}\)
Adding all three:
2(A + K + H) = \(\frac{1}{20} + \frac{1}{25} + \frac{1}{50} = \frac{5 + 4 + 2}{100} = \frac{11}{100}\)
A + K + H = \(\frac{11}{200}\)
H = (A + K + H) - (A + K)
= \(\frac{11}{200} - \frac{1}{20}\)
= \(\frac{11 - 10}{200} = \frac{1}{200}\)
So Himanshu alone finishes the work in 200 days.
Hence, 200 days.
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