A, B and C alone can finish a job in 20, 25 and 30 days, respectively.

A, B and C alone can finish a job in 20, 25 and 30 days, respectively. A and B together start doing the job. However, they leave it after 10 days. The remaining part of the job is finished by C alone. How many days did C take to finish the job ?

4 days
3 days
5 days
6 days
This question was previously asked in
UPSC CISF-AC-EXE – 2023
The correct answer is 3 days. This is the time C took to complete the remaining part of the job after A and B had worked for 10 days.
– A’s daily work rate = 1/20 of the job.
– B’s daily work rate = 1/25 of the job.
– C’s daily work rate = 1/30 of the job.
– A and B work together for 10 days.
– Combined daily work rate of A and B = (1/20) + (1/25) = (5/100) + (4/100) = 9/100 of the job per day.
– Work done by A and B in 10 days = (9/100) * 10 = 90/100 = 9/10 of the job.
– Remaining part of the job = Total job – Work done by A and B = 1 – 9/10 = 1/10 of the job.
– C finishes the remaining 1/10 of the job alone.
– Time taken by C = Remaining work / C’s daily work rate.
– Time taken by C = (1/10) / (1/30) = (1/10) * 30 = 30/10 = 3 days.
This is a standard work and time problem. The key is to calculate the work rate of each individual and the combined work rate when they work together. Then calculate the portion of the job done in a given time, the remaining work, and the time taken to complete the remaining work by the specified person.
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