# Work Time : Rates Practice

This aptitude practice question is a Work Time problem solving question. Concept tested: The crux of solving this question entails framing proper equations from the information given in the word problem.

## Question : Part 1

Working together, A and B can do a job in 6 days. B and C can do the same job in 10 days, while C and A can do it in 7.5 days. How long will it take if all A, B, and C work together to complete the job?

1. 8 days
2. 5 days
3. 3 days
4. 7 days

Correct Answer      Choice (2). If all 3 worked together, the will complete the job in 5 days.

We know that if A and B work together, they can complete the job in 6 days. Therefore, if all three of them A, B and C work together the number of days it will take to complete the job will surely be less than 6 days. Hence, we can eliminate answer choices (1) and (4) right away.

Let A be the number of days that A will take to complete the job if A worked alone, B days for B to complete the job if B worked alone and C days for C to complete the job if C worked alone.

A and B can do a job in 6 days. They complete $$frac{1}{6}^{th}$ of the job in a day. i.e., $\frac{1}{A}$ + $\frac{1}{B}$ = $\frac{1}{6}$ ------$1)
Similarly, B and C will complete $$frac{1}{10}^{th}$ of the job in a day. i.e., $\frac{1}{B}$ + $\frac{1}{C}$ = $\frac{1}{10}$ ------$2)
And C and A will complete $$frac{1}{7.5}$ or $\frac{2}{15}^{th}$ of the job in a day i.e., $\frac{1}{C}$ + $\frac{1}{A}$ = $\frac{2}{15}$ ------$3).

Adding (1), (2) and (3) we get $$frac{1}{A}$ + $\frac{1}{B}$ + $\frac{1}{B}$ + $\frac{1}{C}$ + $\frac{1}{C}$ + $\frac{1}{A}$ = $\frac{1}{6}$ + $\frac{1}{10}$ + $\frac{2}{15}$ => $\frac{2}{A}$ + $\frac{2}{B}$ = $\frac{2}{C}$ = $\frac{5 + 3 + 4}{30}$ = $\frac{12}{30}$ Or $\frac{1}{A}$ + $\frac{1}{B}$ + $\frac{1}{C}$ = $\frac{6}{30}$ = $\frac{1}{5}$. i.e., working together, A, B and C complete 1/5th of the job in a day. Therefore, they will complete the job in 5 days. The correct answer is Choice$2).

## Question Part 2

Working together, A and B can do a job in 6 days. B and C can do the same job in 10 days, while C and A can do it in 7.5 days. How long will A alone take to complete the job?

1. 8 days
2. 6 days
3. 10 days
4. 20 days

Correct Answer      Choice (3). A alone will take 10 days

From part 1, we know $$frac{1}{A}$ + $\frac{1}{B}$ + $\frac{1}{C}$ = $\frac{1}{5}$ ....$4)
From equation (2) in part 1, we know $$frac{1}{B}$ + $\frac{1}{C}$ = $\frac{1}{10}$ Subtract$2) from (4): $$frac{1}{A}$ + $\frac{1}{B}$ + $\frac{1}{C}$ - {$\frac{1}{B}$ + $\frac{1}{C}$} = $\frac{1}{5}$ - $\frac{1}{10}$ Or $\frac{1}{A}$ = $\frac{2-1}{10}$ = $\frac{1}{10}$ If A completes $\frac{1}{10}$ of the work in a day, A will take 10 days to complete the task if A worked alone. The correct answer is Choice$3).

## Online TANCET MBA CourseTry it Free!

Register in 2 easy steps and start learning in 5 minutes!