A building construction work can be completed by two masons A and B together in 22.5$22.5$ days. Mason A alone can complete the construction work in 24$24$ days less than mason B alone. Then mason A alone will complete the construction work in:

### Core Logic Let the time taken by mason A alone to complete the work be x$x$ days. Mason B takes x + 24$x + 24$ days. Work done by A in 1 day = frac1x$\frac{1}{x}$ Work done by B in 1 day = frac1x + 24$\frac{1}{x + 24}$ ### Step 1: Set up the Rate Equation Since together they finish in 22.5$22.5$ days, their combined work in 1$1$ day is frac122.5 = frac145/2 = frac245$\frac{1}{22.5} = \frac{1}{45/2} = \frac{2}{45}$. So, frac1x + frac1x + 24 = frac245$\frac{1}{x} + \frac{1}{x + 24} = \frac{2}{45}$ ### Step 2: Solve the Quadratic Multiply to clear denominators: fracx + 24 + xx(x + 24) = frac245$$\frac{x + 24 + x}{x(x + 24)} = \frac{2}{45}$$ 45(2x + 24) = 2(x^2 + 24x)$$45(2x + 24) = 2(x^2 + 24x)$$ 90x + 1080 = 2x^2 + 48x$$90x + 1080 = 2x^2 + 48x$$ 2x^2 - 42x - 1080 = 0$$2x^2 - 42x - 1080 = 0$$ x^2 - 21x - 540 = 0$$x^2 - 21x - 540 = 0$$ Factorizing: (x - 36)(x + 15) = 0$$(x - 36)(x + 15) = 0$$ Since time cannot be negative, we reject x = -15$x = -15$. So, x = 36$x = 36$ days. ### Pattern Recognition Standard "Time & Work" reciprocal addition resolves purely to a clean factorizable quadratic. Setting the faster worker to x$x$ prevents dealing with negative bounds in factors. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Maths: Basic Mathematics