Question

A is able to do a piece of work in 10 days and B can do the same work in 15 days. If they can work together for four days, what is the fraction of work left?

• A. \(\frac12\)
• B. \(\frac23\)
• C. \(\frac32\)
• D. \(\frac13\)

Answer 1

The Correct Option is D

Let's solve the problem step by step.
A can do the work in 10 days, so A's work rate is:
\[ \frac{1}{10} \text{ of the work per day} \]
B can do the work in 15 days, so B's work rate is:
\[ \frac{1}{15} \text{ of the work per day} \]
Working together, A and B's combined work rate is:
\[ \frac{1}{10} + \frac{1}{15} = \frac{3}{30} + \frac{2}{30} = \frac{5}{30} = \frac{1}{6} \text{ of the work per day} \]
In 4 days, A and B together can complete:
\[ 4 \times \frac{1}{6} = \frac{4}{6} = \frac{2}{3} \text{ of the work} \]
The fraction of the work left is:
\[ 1 - \frac{2}{3} = \frac{1}{3} \]
Therefore, the fraction of work left is:
Answer: D (\(\frac{1}{3}\))