SSC CGL 2024 Tier-I · 23 September 2024, Shift 1 · Quantitative Aptitude · Question 18 of 97

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 trader offers the following discount schemes on the purchase of a refrigerator. ( I ) a discount of 10% followed by a discount of 8% ( ii ) successive discounts of 12% and 10% ( iii ) two successive discounts of 12% ( iv ) a discount of 20% In which scheme is the selling price the lowest?

(a)(i)
(b)(iv)
(c)(iii)
(d)(ii)

Answer

Why

Correct — C. The question asks for the lowest selling price, so take the marked price as ₹100 and track what the buyer actually pays.

(i) 10% then 8% → 100 × 0.90 = 90 → 90 × 0.92 = ₹82.80
(ii) 12% then 10% → 100 × 0.88 = 88 → 88 × 0.90 = ₹79.20
(iii) 12% then 12% → 100 × 0.88 = 88 → 88 × 0.88 = ₹77.44
(iv) flat 20% → 100 × 0.80 = ₹80.00

₹77.44 is the smallest of the four, so scheme (iii), two successive discounts of 12%, leaves the lowest price. That is option (c).

Why the others are wrong

(a)
(i) — Scheme (i) is the weakest pair: 10% then 8% is an equivalent single discount of 17.2%, leaving ₹82.80 — the highest selling price of the four.
(b)
(iv) — Scheme (iv) looks strongest because 20 is the largest single number on offer, but two cuts of 12% strip 22.56% between them, which is more.
(d)
(ii) — Scheme (ii), 12% then 10%, is an equivalent single discount of 20.8% — better than the flat 20%, but still ₹1.76 dearer than scheme (iii).

Concept

Successive discounts multiply, they do not add. A discount of a% followed by b% leaves the buyer paying (1 − a/100)(1 − b/100) of the marked price.

Expanded, that is a single equivalent discount of a + b − ab/100, always a little less than a + b, because the second cut is taken on an already reduced price.

So 12% twice is 24 − 1.44 = 22.56%, not 24% — and it still beats a flat 20%.

Comparing schemes is faster on ₹100 than on any real price, and the order of two discounts does not matter: 0.90 × 0.92 and 0.92 × 0.90 are the same number.

The paper prints the first scheme as ( I ) and the rest as ( ii ), ( iii ), ( iv ). Read them as (i) to (iv).

Key facts

Two successive discounts of a% and b% equal one discount of (a + b − ab/100)%.
Two discounts of 12% come to 22.56%, not 24%.
Selling price = MP × (1 − a/100) × (1 − b/100), and swapping the two discounts changes nothing.
On a marked price of ₹100 the four schemes cost ₹82.80, ₹79.20, ₹77.44 and ₹80.00 in the order (i) to (iv).

Study next

Single equivalent discount for three successive discountsSuccessive percentage change when a price rises and then fallsMarked price, discount and profit percentage chained in one sum

Common traps

Adding the two rates, 12 + 12 = 24, and calling scheme (iii) a 24% discount.
Assuming a single 20% must beat any pair whose parts are both under 20%.
Stopping at the first scheme that beats 20% instead of costing all four.

SSC prints the schemes as a labelled list and asks which gives the minimum selling price, so the work is four short multiplications rather than one idea.

The same question shape runs on 18 Sep 2024, 09:00, Quant Q.6, where a flat 33% beats both successive pairs, and the single-equivalent-discount version is asked on 17 Sep 2024, 12:30, Quant Q.24.

Related PYQs

No directly related past PYQ was found.