Ramesh can do a piece of work in 40 days, Suresh in 20 days and Mahesh in 15…
2026
Ramesh can do a piece of work in 40 days, Suresh in 20 days and Mahesh in 15 days. They all start the work together, but Ramesh leaves after 4 days and Suresh leaves 3 days before the work is completed. In how many days is the work completed?
- A.
9
- B.
6
- C.
5
- D.
7
Attempted by 4 students.
Show answer & explanation
Correct answer: A
Concept: A worker's daily rate of work is 1 divided by the number of days they need to finish the job alone. When several people share one job for possibly different lengths of time, the job is complete once the sum of each person's (daily rate times days actually worked) equals 1 (one whole job).
Application: Let the total time taken to finish the work be x days. Ramesh's rate is 1/40 per day and he leaves after 4 days, so he contributes 4/40 of the job. Suresh's rate is 1/20 per day and he leaves 3 days before the work finishes, so he works (x - 3) days and contributes (x-3)/20. Mahesh's rate is 1/15 per day and he stays until the work is finished, so he contributes x/15. Together they complete the whole job, so:
4/40 + (x-3)/20 + x/15 = 1
Simplify 4/40 to 1/10, giving 1/10 + (x-3)/20 + x/15 = 1.
Take the LCM of 10, 20 and 15, which is 60, and multiply every term by 60: 6 + 3(x-3) + 4x = 60.
Expand the bracket: 6 + 3x - 9 + 4x = 60.
Combine like terms: 7x - 3 = 60.
Solve for x: 7x = 63, so x = 9.
Cross-check: Substituting x = 9 back into the equation — Ramesh contributes 4/40 = 0.1, Suresh works (9-3) = 6 days contributing 6/20 = 0.3, and Mahesh works all 9 days contributing 9/15 = 0.6. Adding these: 0.1 + 0.3 + 0.6 = 1, confirming the work is exactly completed in 9 days.
