A can do a work in 8 days and B in 12 days. They work together for 3 days. What part of the work is left?
- (a)1⁄4
- (b)5⁄8
- (c)3⁄8
- (d)7⁄24
Answer
Why
Correct — C. Add the one-day rates, run them for 3 days, then subtract from the whole job.
One day together = 1⁄8 + 1⁄12 = 3⁄24 + 2⁄24 = 5⁄24
Work in 3 days = 3 × 5⁄24 = 15⁄24 = 5⁄8
Work left = 1 − 5⁄8 = 3⁄8 → option (c).
Why the others are wrong
- (a)1⁄4 — 1⁄4 left means 3⁄4 done, which takes 3.6 days at 5⁄24 a day. They stop after 3 days, having done 5⁄8.
- (b)5⁄8 — 5⁄8 is the work done, not the work left. The question asks what remains: 1 − 5⁄8 = 3⁄8.
- (d)7⁄24 — 7⁄24 left would mean 17⁄24 done, which needs 3.4 days at 5⁄24 a day. Three days give only 15⁄24.
Concept
In work problems rates add, times do not. A finishes in 8 days, so A does 1⁄8 of the job a day; B does 1⁄12. Together they do 5⁄24 a day.
A second route uses a common total. Take the job as 24 units, the LCM of 8 and 12: A does 3 units a day and B does 2, so 5 together. Three days finish 15 units, leaving 9 of 24 = 3⁄8.
Key facts
- One-day work = 1 ÷ the days needed alone.
- A and B together do 1⁄8 + 1⁄12 = 5⁄24 of the job a day.
- Working together they would finish the whole job in 24⁄5 = 4.8 days.
Study next
Common traps
- Stopping at 5⁄8, the work done, when the question asks for the work left.
- Adding the days, 8 + 12 = 20, instead of the one-day rates.
12 Sep 2025, 09:00, Quant Q.16 is the same item with 15 and 20 days: 7⁄60 a day for 4 days is 7⁄15 done, leaving 8⁄15, and 7⁄15 sits among its options as the work-done trap.
15 Sep 2025, 16:00, Quant Q.14 goes a step further: B leaves after 4 days, and A finishes the remaining 4⁄9 alone in 5 1⁄3 days.
Related PYQs
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