Amit alone can complete a piece of work in 28(1/8) days while Amit and Bhanu together can complete the same work in 9 days. Bhanu started the work and after 5 days Amit joined him. After 6 more days, Amit left and Chaman joined the work and the whole work was completed in 26 days.

Which one of the following statements is true?

Solution

Time taken by Amit to complete the whole work = 225/8 days Let total amount of work = 450 units (LCM of 225 and 18) So, efficiency of Amit = 450/(225/8) = 16 units per day Efficiency of Amit + Bhanu = 450/18 = 25 units per day Efficiency of Bhanu = 25 – 16 = 9 units per day Amount of work done by Bhanu in 5 days 9 × 5 = 45 units Amount of work done by Amit and Bhanu together in 6 days = 6 × 25 = 150 units Amount of work done by Bhanu and Chaman together in 15 days = 450 – 45 – 150 = 255 units So, efficiency of Bhanu and Chaman together = 255/15 = 17 units per day Efficiency of Chaman = 17 – 9 = 8 units per day For option (a): Amount of work done by Amit in 12 days = 12 × 16 = 192 units Amount of work done by Bhanu in 16 days = 16 × 9 = 144 days Amount of work done by Chaman in 14(3/4) days = 59/4 × 8 = 118 units Total work done by Amit, Bhanu and Chaman together = 192 + 144 + 118 = 454 units > 450 units So, option (a) cannot be the answer. For option (b): Efficiency of Chaman = 2.5 × 8 = 20 units per day Time taken by Chaman to complete the whole work = 450/20 = 22.5 days So, option (b) cannot be the answer. For option (c): Desired time = (0.64 × 450)/(16 + 8) = 12 days