# Moderate Time and Work Solved QuestionAptitude Discussion

Common Information

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.

 Q. Common Information Question: 1/2 How many days will it take if all A, B and C work together to complete the job?
 ✖ A. 8 ✔ B. 5 ✖ C. 3 ✖ D. 7

Solution:
Option(B) is correct

Even before you start working on the problem, check out if you can eliminate some answer choices as impossible.

We know that if A and B alone work, 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 alone, B days for B to complete the job alone and C days for C to complete the job alone.

A and B can do a job in 6 days. They complete $\left(\dfrac{1}{6}\right)^{th}$ of the job in a day

$\dfrac{1}{A}+\dfrac{1}{B}=\dfrac{1}{6}$........(1)

Similarly, B and C will complete $\left(\dfrac{1}{10}\right)^{th}$ of the job in a day.

$\dfrac{1}{C}+\dfrac{1}{B}=\dfrac{1}{10}$.....(2)

And C and A will complete $\dfrac{1}{7.5}$ or $\left(\dfrac{2}{15}\right)^{th}$of the job in a day

$\dfrac{1}{C}+\dfrac{1}{A}=\dfrac{2}{15}$......(3)

Adding (1), (2) and (3) we get:

$\dfrac{2}{A}+\dfrac{2}{B}+\dfrac{2}{C}=\dfrac{5+3+4}{30}$

$\dfrac{1}{A}+\dfrac{1}{B}+\dfrac{1}{C}=\dfrac{1}{5}$

i.e working together, A, B and C complete $\left(\dfrac{1}{5}\right)^{th}$ of the job in a day.

Therefore, they will complete the job in 5 days.

Edit: For an alternative solution, check comment by Aida.

## (1) Comment(s)

Aida
()

$2(A+B+C)=\dfrac{1}{6} + \dfrac{1}{10} +\dfrac{1}{7.5}$

$2(A+B+C)=\dfrac{10}{60} +\dfrac{6}{60} +\dfrac{8}{60}=\dfrac{24}{60}$

$(A+B+C)=\dfrac{24}{60} : 2$ $= \dfrac{24}{120} \text{ in a day}$

Whole work $\dfrac{120}{24}= \textbf{5 days}$