Q26 / 75 · JEE Main 2026 (23 January Shift 1) · Mathematics
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 :
- A30 days
- Correct answerB36 days
- C24 days
- D42 days
Solution
Let A take $a$ days and B take $a + 24$ days.
Together: $\frac{1}{a} + \frac{1}{a+24} = \frac{1}{22.5} = \frac{2}{45}$.
$\frac{2a+24}{a(a+24)} = \frac{2}{45}$
$45(2a+24) = 2a(a+24)$
$90a + 1080 = 2a^2 + 48a$
$a^2 - 21a - 540 = 0$
$(a-36)(a+15) = 0 \Rightarrow a = 36$.
Mason A alone completes the work in 36 days.
Together: $\frac{1}{a} + \frac{1}{a+24} = \frac{1}{22.5} = \frac{2}{45}$.
$\frac{2a+24}{a(a+24)} = \frac{2}{45}$
$45(2a+24) = 2a(a+24)$
$90a + 1080 = 2a^2 + 48a$
$a^2 - 21a - 540 = 0$
$(a-36)(a+15) = 0 \Rightarrow a = 36$.
Mason A alone completes the work in 36 days.
Hence, the correct answer is option: 'B'.