A building construction work can be completed by two masons A and B together in 22.5 days. [2026]

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Solution

Q.
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: [2026]

1 24 days

2 36 days

3 42 days

4 30 days

Ans.
(2)

$Let time taken by mason A alone to complete the work be x days.$

$So, mason B alone takes (x + 24) days.$

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

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

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

So, $\frac{1}{x} + \frac{1}{x + 24} = \frac{1}{22.5} = \frac{2}{45}$

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

$\Rightarrow \frac{2 x + 24}{x (x + 24)} = \frac{2}{45}$

$45 (2 x + 24) = 2 x (x + 24)$

$90 x + 1080 = 2 x^{2} + 48 x$

$2 x^{2} - 42 x - 1080 = 0$

$x^{2} - 21 x - 540 = 0$

$x = 36 or x = - 15$

$x = - 15 (rejected)$

$Ans. = 36 option (2)$

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