Jitesh and Kamal can complete a certain piece of work in 9 and 12 days…
2025
Jitesh and Kamal can complete a certain piece of work in 9 and 12 days respectively. They started to work together, and after 5 days, Kamal left. In how many days will Jitesh complete the remaining work?
- A.
0.25
- B.
0.75
- C.
1
- D.
1.5
Show answer & explanation
Correct answer: A
Work-rate method: if a person completes a job in T days, their work rate is 1/T of the job per day. When two people work together, their combined rate is the sum of their individual rates, and the work completed over any period equals rate multiplied by time.
Jitesh's rate = 1/9 of the work per day; Kamal's rate = 1/12 of the work per day.
Combined rate working together = 1/9 + 1/12 = 4/36 + 3/36 = 7/36 of the work per day.
Work completed together in 5 days = 5 x 7/36 = 35/36 of the work.
Remaining work after Kamal leaves = 1 - 35/36 = 1/36 of the work.
Time for Jitesh alone to finish 1/36 of the work at his rate of 1/9 per day = (1/36) / (1/9) = 9/36 = 1/4 day = 0.25 days.
Cross-check with the LCM method: take total work as 36 units (LCM of 9 and 12). Jitesh's rate = 36/9 = 4 units/day, Kamal's rate = 36/12 = 3 units/day, combined = 7 units/day. In 5 days together they finish 35 units, leaving 1 unit. At 4 units/day, Jitesh needs 1/4 = 0.25 day to finish the remaining 1 unit, confirming the same result.