Question:medium
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 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?
Updated On: Jul 16, 2026
- \(\frac12\)
- \(\frac23\)
- \(\frac32\)
- \(\frac13\)
Show Solution
The Correct Option is D
Solution and Explanation
Step 1: Take the work as 30 units.
Since A takes 10 days and B takes 15 days, using 30 units (the LCM) gives A a rate of 3 units a day and B a rate of 2 units a day.
Step 2: Find the work done in 4 days.
Together they do \( 3 + 2 = 5 \) units a day, so in 4 days they finish \( 5 \times 4 = 20 \) units.
Step 3: Find what is left.
Work left \( = 30 - 20 = 10 \) units, which is \( \frac{10}{30} = \frac{1}{3} \) of the job. \[ \boxed{\frac{1}{3}} \]
Since A takes 10 days and B takes 15 days, using 30 units (the LCM) gives A a rate of 3 units a day and B a rate of 2 units a day.
Step 2: Find the work done in 4 days.
Together they do \( 3 + 2 = 5 \) units a day, so in 4 days they finish \( 5 \times 4 = 20 \) units.
Step 3: Find what is left.
Work left \( = 30 - 20 = 10 \) units, which is \( \frac{10}{30} = \frac{1}{3} \) of the job. \[ \boxed{\frac{1}{3}} \]
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