JEE Main · 2026 · 23 Jan 2026 · Shift 1 · Quadratic Equations and Inequalities

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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:

(A)24 days
(B)42 days
(C)30 days
(D)36 days✓ Correct

Answer: (D)

Solution

Let A complete the work alone in

x

days, then B takes

x + 24

days.

Work rates: A does

\frac{1}{x}

per day, B does

\frac{1}{x + 24}

per day.

Together:

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

.

Multiplying through:

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

, so

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

.

Simplifying:

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

, giving

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

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

.

Factoring:

(x - 36) (x + 15) = 0

, so

x = 36

(rejecting

x = - 15

JEE Main · 2026 · 23 Jan 2026 · Shift 1 · Single correct option

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JEE Main · 2026 · 23 Jan 2026 · Shift 1 · Quadratic Equations and Inequalities

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