Question

Anil alone can do a job in 20 days while Sunil alone can do it in 40 days. Anil starts the job, and after 3 days, Sunil joins him. Again, after a few more days, Bimal joins them and they together finish the job. If Bimal has done 10% of the job, then in how many days was the job done?

a-13
b-12
c-15
d-14

Answer 1

Anil and Sunil work together to complete 90% of the job, and the remaining 10% of the job is completed when Bimal joins them. The job is completed in 15 days.

Step-by-step explanation:

Let's first find the individual rates of work for Anil and Sunil:

Anil can complete the job in 20 days, so his work rate per day is 1/20 of the job.

Sunil can complete the job in 40 days, so his work rate per day is 1/40 of the job.

Anil works alone for 3 days, so he completes 3/20 of the job. The remaining part of the job is 1-3/20 = 17/20.

When Sunil joins, their combined work rate per day is (1/20 + 1/40) = 3/40 of the job.

Let's define the number of days it takes for them to complete the remaining 17/20 of the job as 'x'.

So, in 'x' days, they can complete (3/40)*x = 17/20 of the job.

Now, Bimal joins when 10% of the job is completed. Since he has done 10% of the job, the remaining part is 1-10% = 90%.

So, we have (3/40)*x = 0.9.

Solving for 'x', we get x = 0.9/(3/40) = 12.

Therefore, the job is completed in 3 days (Anil working alone) + 12 days (Anil and Sunil working together) = 15 days. So, the answer is option (c) 15.