A is able to complete a task in 15 days, while B takes 20 days to finish the same task. If they collaborate and work together for 4 days, what fraction of the work will still remain?
- (a)1⁄4
- (b)7⁄15
- (c)8⁄15
- (d)11⁄15
Answer
Why
Correct — C. Take the total work as the LCM of 15 and 20 = 60 units.
A's rate = 60 ÷ 15 = 4 units a day
B's rate = 60 ÷ 20 = 3 units a day
Together = 7 units a day
In 4 days: 7 × 4 = 28 units done
Left = 60 − 28 = 32 units = 32⁄60 = 8⁄15 → option (c).
Why the others are wrong
- (a)1⁄4 — 1⁄4 left means 3⁄4 done, which at 7⁄60 of the work a day takes about 6.4 days, not 4.
- (b)7⁄15 — 7⁄15 is the work done — 28 of 60 units — not the work left. The question asks what remains: 1 − 7⁄15 = 8⁄15.
- (d)11⁄15 — 11⁄15 is what remains if only A works the 4 days: A alone does 4⁄15. It drops B's 12 units.
Concept
Work problems become arithmetic once the whole job is a number of units. The LCM of the two times gives whole-number daily rates: A 4 units, B 3 units, out of 60.
Rates add when people work together; days do not. Together they do 7 units a day, so the whole job would take 60⁄7 ≈ 8.6 days.
The question asks for the fraction left, so subtract the work done from the whole.
Key facts
- A's one-day work = 1⁄15, B's = 1⁄20, together 1⁄15 + 1⁄20 = 7⁄60.
- In 4 days they finish 28⁄60 = 7⁄15 of the task.
- Work remaining = 1 − work done = 8⁄15.
Study next
Common traps
- Adding the days (15 + 20 = 35) instead of the daily rates.
- Answering with the work done, 7⁄15, when the question asks what remains.
The same set-up with 12 and 16 days, worked together for 6 days, is on 19 Sep 2024, 12:30, Quant Q.14. There 7⁄48 of the work a day for 6 days completes 7⁄8, leaving 1⁄8.
Related PYQs
No directly related past PYQ was found.