Answer: D
Let Mahim take \(x\) hours to clean the garden alone. ∴ Majid takes \((x + 3)\) hours to clean the same garden alone. So, Mahim cleans \(\cfrac{1}{x}\) of the garden in 1 hour. And Majid cleans \(\cfrac{1}{x + 3}\) of the garden in 1 hour. ∴ Together, they clean \(\cfrac{1}{x} + \cfrac{1}{x + 3}\) of the garden in 1 hour. ∴ According to the question: \[ 2\left[\cfrac{1}{x} + \cfrac{1}{x + 3}\right] = 1 \] \[ 2\left[\cfrac{x + 3 + x}{x(x + 3)}\right] = 1 \] \[ 2\left[\cfrac{2x + 3}{x(x + 3)}\right] = 1 \] \[ x(x + 3) = 2(2x + 3) \] \[ x^2 + 3x = 4x + 6 \] \[ x^2 + 3x - 4x - 6 = 0 \] \[ x^2 - x - 6 = 0 \] \[ x^2 - 3x + 2x - 6 = 0 \] \[ x(x - 3) + 2(x - 3) = 0 \] \[ (x - 3)(x + 2) = 0 \] ∴ Either \((x - 3) = 0\) or \((x + 2) = 0\) When \((x - 3) = 0\), then \(x = 3\) When \((x + 2) = 0\), then \(x = -2\) [But time cannot be negative] ∴ Mahim takes 3 hours to clean the garden alone, and Majid takes \(3 + 3 = 6\) hours to do it alone.
Let Mahim take \(x\) hours to clean the garden alone. ∴ Majid takes \((x + 3)\) hours to clean the same garden alone. So, Mahim cleans \(\cfrac{1}{x}\) of the garden in 1 hour. And Majid cleans \(\cfrac{1}{x + 3}\) of the garden in 1 hour. ∴ Together, they clean \(\cfrac{1}{x} + \cfrac{1}{x + 3}\) of the garden in 1 hour. ∴ According to the question: \[ 2\left[\cfrac{1}{x} + \cfrac{1}{x + 3}\right] = 1 \] \[ 2\left[\cfrac{x + 3 + x}{x(x + 3)}\right] = 1 \] \[ 2\left[\cfrac{2x + 3}{x(x + 3)}\right] = 1 \] \[ x(x + 3) = 2(2x + 3) \] \[ x^2 + 3x = 4x + 6 \] \[ x^2 + 3x - 4x - 6 = 0 \] \[ x^2 - x - 6 = 0 \] \[ x^2 - 3x + 2x - 6 = 0 \] \[ x(x - 3) + 2(x - 3) = 0 \] \[ (x - 3)(x + 2) = 0 \] ∴ Either \((x - 3) = 0\) or \((x + 2) = 0\) When \((x - 3) = 0\), then \(x = 3\) When \((x + 2) = 0\), then \(x = -2\) [But time cannot be negative] ∴ Mahim takes 3 hours to clean the garden alone, and Majid takes \(3 + 3 = 6\) hours to do it alone.