SSC CGL 2025 Tier-I · 15 September 2025, Shift 3 · Quantitative Aptitude · Question 14 of 100

We transcribed this text from the pictures on a candidate's response sheet for this shift; the answer is the key SSC colour-marked on that sheet. Solution last reviewed 11 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. From 2025 the candidate response sheet prints every question and option as a picture, so the text here is transcribed from those pictures for this shift and checked against them independently; where the layout carries meaning, the picture is shown as well. Each answer is the key SSC colour-marked on that sheet. SSC released a tentative key for challenge and later its final one, both only to candidates behind a login, and the sheet does not say which of the two it carries. The solutions are written by UnlockIAS.

A and B can complete a task in 12 days and 18 days, respectively. They begin the work together, but B leaves after 4 days. How many more days will A take to finish the remaining work?

(a)5 1⁄3 days
(b)2 3⁄4 days
(c)1 1⁄5 days
(d)8 6⁄7 days

Answer

Why

Correct — A.
Take the task as 36 units (LCM of 12 and 18).
A's rate: 36 ÷ 12 = 3 units a day
B's rate: 36 ÷ 18 = 2 units a day

Together for 4 days: (3 + 2) × 4 = 20 units
Left for A: 36 − 20 = 16 units
A alone: 16 ÷ 3 = 5 1⁄3 days → option (a)

Why the others are wrong

(b)
2 3⁄4 days — 2 3⁄4 days at A's 3 units a day covers only 8.25 units, about half of the 16 units left after the first 4 days.
(c)
1 1⁄5 days — 1 1⁄5 days gives A time for just 3.6 units, far short of the 16 units that remain once B has gone.
(d)
8 6⁄7 days — 8 6⁄7 days would let A do about 26.6 units, more than the 16 units left, so it overshoots the remaining work.

Concept

Pick a total work that both times divide into, here 36 units, and each worker's time becomes a daily rate: A 3 units, B 2 units.

Work done = rate × days. The first 4 days run at the combined rate of 5 units a day; after B leaves, only A's 3 units a day apply to what is left.

The question asks how many more days A takes after B leaves. The whole job lasts 4 + 5 1⁄3 = 9 1⁄3 days, which is not what is asked.

In fractions: together they do 1⁄12 + 1⁄18 = 5⁄36 a day, 20⁄36 in 4 days, leaving 16⁄36 = 4⁄9 for A at 1⁄12 a day, which is 48⁄9 = 5 1⁄3 days.

Key facts

Daily rate = 1 ÷ days to finish alone: A does 1⁄12 of the task a day, B 1⁄18.
Rates add when people work together: 1⁄12 + 1⁄18 = 5⁄36 a day.
Time for the remainder = work left ÷ rate of whoever is still working.

Study next

Fraction of work left after two people work together for a set number of daysFinding how long one worker stayed when the other finishes the restWork problems with three workers joining or leaving at different times

Common traps

Adding the first 4 days and answering 9 1⁄3 days, when the question asks only for the extra days.
Dividing the 16 units left by B's rate, 16 ÷ 2 = 8 days, when it is B who has left.

14 Sep 2025, 09:00, Quant Q.15 stops at the first half of this working: A (8 days) and B (12 days) work together for 3 days on a 24-unit task, finishing 15 units and leaving the keyed 3⁄8.

18 Sep 2025, 12:30, Quant Q.5 runs it backwards: B (35 days) finishes in 17 days after A (28 days) leaves, so 140 − 68 = 72 units were done together at 9 a day, the keyed 8 days.

Related PYQs

No directly related past PYQ was found.

Topic: Time & Work — all 48 SSC CGL questions on it, every solved shift.