SSC CGL 2024 Tier-I · 25 September 2024, Shift 2 · Quantitative Aptitude · Question 18 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 10 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.

During a new-year sale, a shopkeeper offers a discount scheme to his customers, ‘Buy 5 Sweaters, Get 2 Sweaters Free’. Find the effective percentage discount given by the shopkeeper.

Answer

Why

Correct — A. The options are printed as images; option (a) reads 28 4⁄7 %. The customer pays for 5 sweaters but carries home 7, so 2 of those 7 are free.

Sweaters paid for = 5, sweaters received = 5 + 2 = 7
Free share = 2 out of 7
Discount% = 2 ⁄ 7 × 100 = 200⁄7 = 28 4⁄7 % → option (a)

Check it with money: at a marked price of ₹1 each the list value is ₹7 and the customer pays ₹5, so ₹2 is forgone on ₹7.

Why the others are wrong

(b)
Option (b) reads 22 2⁄9 %, which is 2⁄9. A denominator of 9 belongs to an offer of buy 7, get 2 free. Here the customer walks out with 7 sweaters, not 9.
(c)
Option (c) reads 25%, which is 2⁄8 — the discount on buy 6, get 2 free. It also sits just below the true 28.57%, so an eyeballed answer lands here.
(d)
Option (d) reads 30%. Two free items make 30% only on a total of 6⅔ items, which no whole-number offer produces. 200⁄7 is 28.57%, not 30.

Concept

A free-goods offer is a discount because the buyer pays for fewer items than they receive.

The rule: discount % = free items ⁄ total items received × 100. The denominator is what the customer walks away with, not what they pay for.

Buy 5, get 2 free hands over 7 for the price of 5, so 2⁄7 of the list value is forgone. Put the other way, the buyer pays 5⁄7 of list value, which is 71 3⁄7 %.

The tempting denominator is 5, the number bought. That gives 2⁄5 = 40%, which is not among the four options — a signal that the paper wants the 7-item total.

Key facts

Buy m, get n free is a discount of n ⁄ (m + n), taken on the list value of all m + n items.
Buy 5, get 2 free = 2⁄7 = 28 4⁄7 %, or 28.571% to three decimals.
The buyer pays 5⁄7 of the list value, which is 71 3⁄7 %.

Study next

Converting buy-m-get-n-free offers into a single discount percentageThe single discount equivalent to two successive discountsMarked price, discount and the profit that survives the discount

Common traps

Dividing the 2 free sweaters by the 5 paid for, which gives 40%
Rounding 200⁄7 up to 30% instead of reading the mixed fraction off the options
Mistaking the printed option images for decimals when they are mixed fractions

SSC more often prints this topic as successive discounts than as a free-goods offer. The single-equivalent form is asked at 10 Sep 2024, 12:30, Quant Q.14 (two successive discounts of 40% and 30%) and at 17 Sep 2024, 12:30, Quant Q.24 (40% followed by a further 20%).

Related PYQs

No directly related past PYQ was found.