A building construction work can be completed by two masons A and B together in 22.5 days. Mason A a

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A building construction work can be completed by two masons A and B together in 22.5 days. Mason A alone can complete the construction work in 24 days less than mason B alone. Then mason A alone will complete the construction work in:

Accepted Answer

Let time taken by mason a alone to complete the work be in x days so, mason B along take $x + 24$ days

work done by A in 1 day $= \frac{1}{x}$

work done by B in 1 day $= \frac{1}{x + 24}$

so work done by $A + B$ in 1 day $= \frac{1}{22.5}$

So, $\frac{1}{x} + \frac{1}{x + 24} = \frac{2}{45}$

$${x^{2} - 21x - 540 = 0 }{x = 36\& }$$$x = - 15($ rejected $)$

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