Rajeshwar can do a piece of work in 12 days, Vikram in 6 days and Tiger in 15 days. They all start the work together, but Rajeshwar leaves after 2 days and Vikram leaves 3 days before the work is completed. In how many days is the work completed?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. .
total work = (LCM of 12,6,15) = 60 units.
Efficiency (units/day):
Rajeshwar = 60×(1/12) = 5
Vikram = 60×(1/6) = 10
Tiger = 60×(1/15) = 4
Together = 19 units/day.
First 2 days (all three): 2×19 = 38 units
Remaining = 60 − 38 = 22 units.
After 2 days Rajeshwar leaves. Let there be y days when Vikram+Tiger work, then last 3 days only Tiger works.
Vikram+Tiger rate = 10 + 4 = 14 units/day
So 22 = 14y + 3 × 4 = 14y + 12
→ 14y = 10
→ y = 5/7 day.
Total time = 2 + y + 3 = 5 + 5/7 = days.