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Question
A can do a piece of work in ‘x’ days and B can do the same work in (x + 16) days. If both working together can do it in 15 days. Calculate ‘x’.
Solution
Work done by A in one day = `1/x`
Work done by B in one day = `1/(x + 16)`
Together A and B can do the work in 15 days.
Therefore, we have
`1/x + 1/(x + 16) = 1/15`
`(x + 16 + x)/(x (x + 16)) = 1/15`
`(2x + 16)/(x^2 + 16x) = 1/15`
`30x + 240 = x^2 + 16x`
`x^2 - 14x - 240 = 0`
`(x - 24)(x + 10) = 0`
x = 24, –10
Since, x cannot be negative
Thus, x = 24
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