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work and wages(self doubts)

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A can do a certain work in the same time in which B and C together can do it.If A and B together could do it in 10 days and C can alone in 50 days,then B  alone in 50 days, then B alone could do it in:
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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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