XAT 2018 — QA & DI Question 2
Abdul, Bimal, Charlie and Dilbar can finish a task in 10, 12, 15 and 18 days respectively. They can either choose to work or remain absent on a particular day. If 50 percent of the total work gets completed after 3 days, then, which of the following options is possible?
Answer & solution
- A
Each of them worked for exactly 2 days.
- B
Bimal and Dilbar worked for 1 day each, Charlie worked for 2 days and Abdul worked for all 3 days.
- C
Abdul and Charlie worked for 2 days each, Dilbar worked for 1 day and Bimal worked for all 3 days.
- D
Abdul and Dilbar worked for 2 days each, Charlie worked for 1 day and Bimal worked for all 3 days.
Abdul and Charlie worked for 1 day each, Bimal worked for 2 days and Dilbar worked for all 3 days.
Let the total units of work = LCM of (10, 12, 15 and 18) = 180
Therefore, efficiencies of Abdul, Bimal, Charlie and Dilbar individually in one day will be 18 units, 15 units, 12 units and 10 units per day respectively.
Let us check options now:
Option (a): Total work done = 2 × (18 + 15 + 12 + 10)
= 110 units
Option (b): Total work done = 1 × (15 + 10) + 2 × 12 + 3 × 18
= 25 + 24 + 54 = 103 units
Option (c): Total work done = 2 × (18 + 2) + 1 × 10 + 3 × 15
= 40 + 10 + 45 = 95 units
Option (d): Total work done = 2 × (18 + 10) + 1 × 12 + 3 × 15
= 56 + 12 + 45 = 113 units
Option (e): Total work done = 1 × (18 + 12) + 2 × 15 + 3 × 10
= 30 + 30 + 30 = 90 units
Hence, option (e).