JEE Main 2026 — Jan 23, Shift 1 — Mathematics solution

JEE Main2026Jan 23, Shift 1Mathematics

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 :

A
$24$ days
B
$42$ days
C
$30$ days
D
$36$ days

Solution

Let A alone take $x$ days; B takes $x + 24$ days. Combined rate:

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

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

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

Factoring: $(x - 36) (x + 15) = 0$ , so $x = 36$ (rejecting negative).

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