JEE MAIN Time And Work Previous Year Questions (PYQs)
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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:
1
2
3
4
Solution
Let time taken by $B = x$ days
Then time by $A = x - 24$
$\frac{1}{x} + \frac{1}{x-24} = \frac{1}{22.5}$
$\frac{2x - 24}{x(x-24)} = \frac{2}{45}$
$45(2x - 24) = 2x(x - 24)$
$90x - 1080 = 2x^2 - 48x$
$2x^2 - 138x + 1080 = 0$
$x = 60$
$\Rightarrow A = 60 - 24 = 36$
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