JEE Mathematics 2026 Question with Solution

Given: Let mason $A$ alone take $x$ days and mason $B$ alone take $y$ days.

• Together they complete the work in $22.5$ days.
• Mason $A$ takes $24$ days less than mason $B$, so $y = x + 24$.

Find: The number of days taken by mason $A$ alone.

This is a work-time problem. In one day, mason $A$ completes $\frac{1}{x}$ of the work and mason $B$ completes $\frac{1}{y}$ of the work. Together, they complete $\frac{1}{22.5} = \frac{2}{45}$ of the work per day.

Using the given relation:

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

with

$$y = x + 24$$

Substitute $y$ into the work equation:

$$\frac{1}{x} + \frac{1}{x+24} = \frac{2}{45}$$ $$\frac{x + 24 + x}{x(x+24)} = \frac{2}{45}$$ $$\frac{2x + 24}{x^2 + 24x} = \frac{2}{45}$$ $$45(x + 12) = x^2 + 24x$$ $$45x + 540 = x^2 + 24x$$ $$x^2 - 21x - 540 = 0$$

Factorizing:

$$x^2 - 36x + 15x - 540 = 0$$ $$x(x-36) + 15(x-36) = 0$$ $$(x-36)(x+15) = 0$$

So, $x = 36$ or $x = -15$. Since time cannot be negative, $x = 36$.

Therefore, mason A alone will complete the work in $36$ days. The correct option is C.

Given: Mason $A$ takes $x$ days and mason $B$ takes $x+24$ days.

Find: Which option satisfies the combined work rate $\frac{1}{22.5} = \frac{2}{45}$.

Check option C: if $x = 36$, then $y = 60$.

$$\frac{1}{36} + \frac{1}{60} = \frac{5+3}{180} = \frac{8}{180} = \frac{2}{45}$$

This matches the required combined rate.

Therefore, mason A alone completes the work in $36$ days, so the correct option is C.