# Work Time Practice: Word problem

This aptitude practice question in Work Time and pipes cisterns is a problem solving question. Concept tested: Framing equations for work time and solving those equations. A word problem in rates.

## Question

Shyam can do a job in 20 days, Ram in 30 days and Singhal in 60 days. If Shyam is helped by Ram and Singhal every 3rd day, how long will it take for them to complete the job?

1. 12 days
2. 5 days
3. 15 days
4. 10 days

Correct Answer      Choice (3). They will complete the work in 15 days

Shyam completes the job in 20 days. So, Shyam does $$frac{1}{20}$th of the job in a day. Ram completes the job in 30 days. So, Ram does $\frac{1}{30}$th of the job in a day. Singhal completes the job in 60 days. So, Singhal does $\frac{1}{60}$th of the job in a day. As Shyam is helped by Ram and Singhal every third day, Shyam works for 3 days while Ram and Singhal work for 1 day in every 3 days. If in 1 day Shyam completes $\frac{1}{20}$th of the job, in 3 days he will complete $\frac{3}{20}$th of the job. Therefore, the amount of work done in 3 days by Shyam, Ram and Singhal = $\frac{3}{20}$ + $\frac{1}{30}$ + $\frac{1}{60}$ = $\frac{9 + 2 + 1}{60}$ = $\frac{12}{60}$ = $\frac {1}{5}^{th}$ of the job in 3 days. Hence, it will take them 5 times the amount of time = 3 * 5 = 15 days to complete the entire job. The correct answer is Choice$3).

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