Question

Work done by A in one day is half of the work by B in one day. Work done by B is half on the work done by C in one day. If C alone can do the work in 7 days, then in how many days can A, B and C together complete the work ?

• A. 4
• B. 14
• C. 21
• D. 28

Answer 1

The Correct Option is A

To solve the problem, we need to determine the collective work rate of A, B, and C and then use that to find how many days it will take for them to complete the work together.

Let's start by understanding the daily work contributions:

1. C can complete the work in 7 days, so C does $\frac{1}{7}$ of the work in a day.

2. B does half the work that C does in a day, so B does $\frac{1}{2}\times \frac{1}{7}=\frac{1}{14}$ of the work in a day.

3. A does half of the work that B does in a day, so A does $\frac{1}{2}\times \frac{1}{14}=\frac{1}{28}$ of the work in a day.

Now, let's determine their combined work rate:

The combined work done by A, B, and C in a day is $\frac{1}{28}+\frac{1}{14}+\frac{1}{7}=\frac{1}{28}+\frac{2}{28}+\frac{4}{28}=\frac{7}{28}$.

Simplify this to get $\frac{1}{4}$. This means together, they can complete $\frac{1}{4}$ of the work in a day.

Therefore, the number of days required for A, B, and C to complete the work together is 4.