SSC CGL 2025 Tier-I · 18 September 2025, Shift 2 · Quantitative Aptitude · Question 5 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.

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A and B can finish a certain job in 28 and 35 days, respectively. They started working together, but A left after a while, and B managed to complete the remaining work in 17 days. How many days did A work before leaving?

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

Answer

Why

Correct — A. Take the job as 140 units, the LCM of 28 and 35.

A's rate: 140 ÷ 28 = 5 units a day
B's rate: 140 ÷ 35 = 4 units a day
Combined rate: 5 + 4 = 9 units a day

B alone for the last 17 days: 17 × 4 = 68 units
Left for the joint spell: 140 − 68 = 72 units
Days A worked: 72 ÷ 9 = 8 days → option (a).

Why the others are wrong

(b)
5 days — Check it: 5 joint days do 5 × 9 = 45 units, leaving 95. B would need 95 ÷ 4 = 23.75 days for that, not 17.
(c)
6 7⁄2 days — Only 8 joint days leave exactly 68 units, which is B's 17 days at 4 a day. 6 7⁄2 days, however its stacked fraction is read, is not 8.
(d)
7 5⁄2 days — 7 5⁄2 is not 8. Taken at face value it is 7 + 2.5 = 9.5 days, and 9.5 joint days leave B only 54.5 units, 13.625 days of work instead of 17.

Concept

Work questions become whole-number sums once the job is set to the LCM of the day counts. Here that is 140 units, so A does 5 a day and B does 4.

The item turns on the second phase: after A leaves, B works alone for 17 days. Subtract B's solo work first. What remains is the joint phase, done at the combined 9 units a day.

Options (c) and (d) are printed as stacked mixed numbers whose fraction part is more than 1: 6 and 7⁄2, 7 and 5⁄2. Taken at face value each is 9.5 days. Neither is 8, so the key is unaffected.

Key facts

Setting the job to the LCM of the individual times (140 for 28 and 35) turns the rates into whole numbers.
Working together, rates add: 5 + 4 = 9 units a day.
Work = rate × time, so B's 17 solo days are 17 × 4 = 68 units.

Study next

Work questions where a second worker joins partway instead of leavingPipes and cisterns where one pipe is closed after some timeSharing wages in proportion to the work each person did

Common traps

Dividing the 72 joint units by A's rate alone (72 ÷ 5 = 14.4), forgetting that B was working during the joint phase too.

15 Sep 2025, 16:00, Quant Q.14 runs it the other way round: A (12 days) and B (18 days) start together, B leaves after 4 days, and the time A needs to finish is keyed 5 1⁄3 days.

Related PYQs

No directly related past PYQ was found.

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