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 (\(\frac{1}{3}\))

Answer 2

We can also check each option by comparing it with what is actually left once A and B have worked together for 4 days, using their combined daily rate.

1. Option A (\(\frac{1}{2}\)): This would mean only half the work got done in 4 days, which does not match A and B's combined rate of \( \frac{1}{6} \) of the work a day.
2. Option B (\(\frac{2}{3}\)): This is actually the fraction of work completed in 4 days, not the fraction left, so it does not answer the question asked.
3. Option C (\(\frac{3}{2}\)): A fraction greater than 1 is impossible here since work left can never exceed the whole job, so this is ruled out immediately.
4. Option D (\(\frac{1}{3}\)): Since \( \frac{2}{3} \) of the work is finished in 4 days, what remains is \( 1 - \frac{2}{3} = \frac{1}{3} \), matching this option.

Only option D correctly reflects the leftover portion of the work after 4 days together.

Let's summarize:

• A and B together finish \( \frac{2}{3} \) of the work in 4 days.
• What is left is the complement of that, \( \frac{1}{3} \).

Therefore, the correct answer is D (\(\frac{1}{3}\)).