When working alone, Ansh takes 12 more days than time taken by Ansh and Balu together to finish certain work. If Ansh is 50% more efficient than Balu, then find the time taken by Balu to finish the work alone

Let the time taken by Ansh to finish the work alone be '2x' days. Ratio of efficiencies of Ansh and Balu = 3:2 Since, the work done is same, ratio of efficiencies of Ansh and Balu will be inverse of the ratio of time taken by Ansh and Balu to finish the work. So, time taken by Balu to finish the work alone = 2x × (3/2) = '3x' days So, time taken by Ansh and Balu to finish the work together = (2x - 12) days ATQ: 1/(2x + 12) = 1/3x + 1/2x or, 1/2(x + 6) = (2x + 3x)/(2x × 3x) or, 3x = 5(x – 6) or, 3x = 5x – 30 or, 2x = 30 or, x = 15 So, time taken by 'B' to finish the work alone = 3x = 15 × 3 = 45 days