Mathematics · Basic Maths

JEE Main 2026 — 23 January, Morning Shift — Question 19

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:

Option A:
24 days
Option B:
42 days
Option C:
30 days
Option D:
36 days
Correct

Answer: D

Step-by-step solution

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 $=\frac{1}{\mathrm{x}}$

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

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

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

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

$\mathrm{x}=36 \&$

$\mathrm{x}=-15($ rejected $)$

Ans. $=36$

Answer key and solution verified before publishing.

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Exam: JEE Main 2026
Paper: 23 January, Morning Shift
Subject: Mathematics
Chapter: Basic Maths
Topic: Basic Arithmetic & Algebra