Durgesh can complete a task alone in 21 days. If Vikash works alone for 8 days and then leaves, Durgesh can finish the remaining work in 7 days. Satish is 25% less efficient than Durgesh. If Vikash and Satish work together for ‘x’ days and then leave, Durgesh can complete the remaining work alone in 6 days. Determine the value of ‘x’.

Answer: A Let the efficiency of Durgesh alone = ‘y’ units/day Then, total work = 21 × y = ‘21y’ units Let the efficiency of Vikash = ‘z’ units/day We have, 8 × z + 7 × y = 21y Or, 8z = 14y So, z:y = 14:8 = 7:4 So, ratio of efficiencies of Vikash  and Durgesh is 7:4, respectively So, efficiency of Vikash = (7y/4) = ‘1.75y’ units/day Efficiency of Satish = y × 0.75 = ‘0.75y’ units/day Combined efficiency of Vikash and Satish = 1.75y + 0.75y = ‘2.5y’ units/day According to the question, 2.5y × x + y × 6 = 21y Or, 6y + 2.5xy = 21y Or, 2.5xy = 15y So, x = 15 ÷ 2.5 = 6