Time and Work Question 2 - CAT 2021
Anu, Vinu and Manu can complete a work alone in 15 days, 12 days and 20 days, respectively. Vinu works everyday. Anu works only on alternate days starting from the first day while Manu works only on alternate days starting from the second day. Then, the number of days needed to complete the work is:
Step-by-Step Explanation
Let the total work be the LCM of 15, 12, and 20, which is 60 units.
Anu's daily efficiency = 60/15 = 4 units/day
Vinu's daily efficiency = 60/12 = 5 units/day
Manu's daily efficiency = 60/20 = 3 units/day
- Map the alternating work schedule step-by-step:
Day 1 (Anu + Vinu): 4 + 5 = 9 units
Day 2 (Manu + Vinu): 3 + 5 = 8 units
Total work completed in one 2-day block = 9 + 8 = 17 units
- Track the blocks required to near completion:
Work done in 3 complete blocks (6 days) = 17 × 3 = 51 units
Remaining Work = 60 − 51 = 9 units
On the 7th day, the cycle resets to the Day 1 roster (Anu + Vinu). Their combined output is exactly 9 units/day, so they finish the remaining 9 units in exactly 1 full day.
Total Time = 6 + 1 = 7 days
Correct Option: D