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JEE Main 202623 JanuaryMorning Shift
Exam
JEE Main
Year
2026
Date
23 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Quadratic Equation

JEE Main 2026 · 23 January · Morning Shift · Mathematics · Quadratic Equation

A building construction work can be completed by two masons A and B...

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 :

Options

  1. A30 days
  2. B36 days
  3. C24 days
  4. D42 days

Correct answer

B. 36 days

Step-by-step solution

Let A take aa days and B take a+24a + 24 days.
Together: 1a+1a+24=122.5=245\frac{1}{a} + \frac{1}{a+24} = \frac{1}{22.5} = \frac{2}{45}.
2a+24a(a+24)=245\frac{2a+24}{a(a+24)} = \frac{2}{45}
45(2a+24)=2a(a+24)45(2a+24) = 2a(a+24)
90a+1080=2a2+48a90a + 1080 = 2a^2 + 48a
a2−21a−540=0a^2 - 21a - 540 = 0
(a−36)(a+15)=0⇒a=36(a-36)(a+15) = 0 \Rightarrow a = 36.
Mason A alone completes the work in 36 days.
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