Amit alone can complete a piece of work in 28(1/8) days

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