SSC CGL 2024 Tier-I · 17 September 2024, Shift 2 · Quantitative Aptitude · Question 24 of 100

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 shopkeeper allows 40% discount on his goods. He further gives 20% discount. What is the single discount equivalent to these two successive discounts?

(a)50%
(b)60%
(c)62%
(d)52%

Answer

Why

Correct — D. Discounts multiply on what is left, they do not add.

After 40% off, the buyer pays 60% of the marked price → factor 0.60.
After a further 20% off that, the buyer pays 80% of the reduced price → factor 0.80.

Net paid = 0.60 × 0.80 = 0.48, that is 48% of the marked price.
Single equivalent discount = 100% − 48% = 52% → option (d).

Formula check: a + b − ab⁄100 = 40 + 20 − (40 × 20)⁄100 = 60 − 8 = 52.

Why the others are wrong

(a)
50% — 50% would leave the buyer paying half the marked price. After the 40% cut, 0.60 of the price remains, so landing on 0.50 needs a second discount of 16⅔%, not 20%.
(b)
60% — 60% is 40 + 20 added straight. That double-counts, because the second 20% comes off the reduced ₹60 and is worth ₹12, not the ₹20 it would be worth on ₹100.
(c)
62% — 62% would leave 38% of the marked price. Starting from 0.60, reaching 0.38 needs a second discount of about 36.7%, far more than the 20% the stem allows.

Concept

A discount series acts on a shrinking base. Each rate is applied to whatever survived the previous cut, so the right operation is multiplying the surviving fractions.

Two discounts of a% and b% leave (1 − a⁄100)(1 − b⁄100) of the marked price, and the single equivalent discount is one minus that.

Written out, the equivalent discount is a + b − ab⁄100. The subtracted ab⁄100 is exactly the overlap you would double-count by adding — 8 percentage points in this item.

Order does not matter, because multiplication commutes: 0.6 × 0.8 = 0.8 × 0.6.

The equivalent single discount is always smaller than the sum of the two rates and larger than either rate alone. Here it has to land between 40% and 60%.

That bracket alone removes two of the four printed options before any arithmetic.

Key facts

Successive discounts of a% and b% equal a single discount of a + b − ab⁄100.
40% and 20% off leave 0.60 × 0.80 = 0.48 of the marked price, so the single discount is 52%.
The equivalent discount always falls short of a + b by exactly ab⁄100.
Reversing the order of two discounts leaves the final price unchanged.

Study next

Extending the multiplier method to three or more discounts in a seriesSuccessive percentage increases, where the sign of the ab⁄100 term flipsMark-up followed by discount, where cost, marked price and selling price are three separate bases

Common traps

Adding the two rates and answering 60%
Applying the second discount to the original marked price instead of the reduced one
Reporting 48%, the fraction the buyer pays, when the stem asks for the discount

SSC asks for the single equivalent of a discount series and varies how many terms it prints.

Two discounts of 40% and 30% are asked at 10 Sep 2024, 12:30, Quant Q.14 (answer 58%). Three-term series run at 25 Sep 2024, 16:00, Quant Q.24 with 15%, 20% and 5% (answer 35.4%) and at 23 Sep 2024, 16:00, Quant Q.21 with 60%, 70% and 80% (answer 97.6%).

Related PYQs

No directly related past PYQ was found.