SSC CGL 2024 Tier-I · 19 September 2024, Shift 2 · Quantitative Aptitude · Question 14 of 99

Text as printed on a candidate's response sheet for this shift; answer per SSC's tentative key as marked on that sheet. Solution last reviewed 6 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. The questions and options here are reproduced as printed on a candidate's own response sheet for this shift — the Commission's text, unchanged. Each answer is SSC's tentative key as marked on that sheet; SSC allowed challenges to it and never publishes a final key. The solutions are written by UnlockIAS.

A and B can do a work in 12 days and 16 days, respectively. If they work together for 6 days, then the fraction of the work left is _________.

Answer

Why

Correct — D. Work in whole units rather than fractions: take the job as LCM(12, 16) = 48 units.

A's rate = 48 ÷ 12 = 4 units a day
B's rate = 48 ÷ 16 = 3 units a day
Together = 4 + 3 = 7 units a day

In 6 days they do 7 × 6 = 42 units
Left = 48 − 42 = 6 units
Fraction left = 6⁄48 = 1⁄8 → option (d), the fourth picture.

Why the others are wrong

(a)
That is the part done, not the part left. 42 of the 48 units are finished and 42⁄48 = 7⁄8, so option (a) answers the question one line too early — what remains is the complement.
(b)
The 7 in option (b) is a daily rate, not a total. A fraction of the job is measured against the whole job, 48 units, so the denominator has to divide 48 — and 7 does not.
(c)
Right numerator, impossible denominator. 6 units remain out of 48, which is 1⁄8; 48 is not divisible by 7 at all, so nothing about this job reduces to sevenths.

Concept

The LCM method replaces fraction arithmetic with counting. Call the job 48 units — the LCM of 12 and 16 — and each worker's daily output becomes a whole number.

Rates add: A does 4 units a day, B does 3, so together they clear 7 units a day. Six days is then a single multiplication.

The last step is the one the stem is really testing. Work done and work left add to 1, so finding 7⁄8 done is not the answer until you subtract.

All four options are pictures on this item — plain fractions with no units — so the deciding word is left in the stem, not anything in the choices.

Key facts

Taking the job as the LCM of the given times turns daily rates into whole numbers.
12 days and 16 days give rates of 4 and 3 units a day out of a 48-unit job.
Working together, A and B clear 7 units a day, so 6 days finishes 42 of 48.
Work done plus work left always equals 1, so 7⁄8 done means 1⁄8 left.

Study next

The LCM total-work method as a replacement for adding 1⁄12 + 1⁄16Finding how many more days the remainder takes when one worker leavesPipes and cisterns, where an outlet carries a negative rate

Common traps

Answering with the work completed when the stem asks for the work left
Adding the days, 12 + 16, instead of adding the daily rates
Adding 1⁄12 + 1⁄16 under time pressure and slipping on the common denominator

The whole difficulty is the phrasing: the arithmetic stops at 42 of 48 units and the stem then asks for what remains.

The same one-day-rate machinery drives the cistern item at 09 Sep 2024, 12:30, Quant Q.25, where pipes M, N and S fill a tank in 25, 50 and 100 minutes and two of them run for a stretch before the third joins.

Related PYQs

No directly related past PYQ was found.