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work and wages(self doubts)

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If A can do a certain amount of work in the same amount of time which B and C would take if they work together and If A and B work together then they can complete the same amount of work in 10 days. If C works alone then the same amount of work would be completed in 50 days,then what would be the number of days B would take to complete the work if he works alone _______.

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1/A = 1/B + 1/C (i)

1/A + 1/B = 1/10 (ii)

It is given that C can alone do the work in 50 days. So, (i) becomes

1/A – 1/B = 1/50 (iii)

Solving (ii) & (iii), we get B = 25 days
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