SSC CGL 2024 Tier-I · 10 September 2024, Shift 2 · Quantitative Aptitude · Question 14 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.

Two successive discounts of 40% and 30% are equal to a single discount of:

(a)60%
(b)70%
(c)35%
(d)58%

Answer

Why

Correct — D. Successive discounts multiply, they do not add.

Take the marked price as ₹100.
after 40% off: 100 × 0.60 = ₹60
after a further 30% off that ₹60: 60 × 0.70 = ₹42

You pay ₹42 of ₹100, so the price fell by
100 − 42 = 58, a single discount of 58% → option (d).

The one-line form for discounts of a% and b%:
a + b − ab⁄100 = 40 + 30 − (40 × 30)⁄100 = 70 − 12 = 58.

Why the others are wrong

(a)
60% — 60% is the fraction of the price surviving the first discount, 0.60, mistaken for the discount itself. After both cuts the survivor is 0.42, so the discount is 58%.
(b)
70% — 70% simply adds 40 and 30. Adding double-counts, because the second discount is charged on the reduced ₹60 and removes ₹18 of the original ₹100 rather than ₹30.
(c)
35% — 35% averages the two figures, (40 + 30) ⁄ 2. An average would be right only if each rate applied to a separate half of the price, which is not what successive means.

Concept

Successive percentage changes multiply their surviving fractions. They never add their percentages.

40% off leaves 0.60 of the price. A further 30% off leaves 0.70 of that. Together they leave 0.60 × 0.70 = 0.42, so 58% has gone.

Order does not matter, because 0.70 × 0.60 is the same product — which is why a shop can stack two coupons either way round and charge the same.

For any two changes a% and b%, the net change is a + b + ab⁄100, a discount entering as a negative percentage.

The single-discount figure is always smaller than the sum and larger than either part. 58 sits between 40 and 70, so any option outside that window is wrong before you calculate — which disposes of 35% straight away.

Key facts

Two successive discounts of a% and b% leave (1 − a⁄100)(1 − b⁄100) of the marked price.
Successive discounts of 40% and 30% equal a single discount of 58%.
The net of two successive changes is a + b + ab⁄100, with discounts signed negative.
Successive discounts commute — 40% then 30% costs the buyer exactly what 30% then 40% costs.

Study next

Successive percentage increases, and why two 50% rises give 125% rather than 100%The equivalent single discount for three successive discountsMarked price, discount and profit percentage combined in one sum

Common traps

Adding the two discounts to 70%.
Charging the second discount on the original price instead of the reduced one.
Carrying the minus sign into the increase version, where the last term is added.

The discount version and the increase version are one sum wearing two hats, and SSC often sets both. In this shift they are adjacent — 10 Sep 2024, 12:30 PM, Quant Q.14 asks for the equivalent single discount and Quant Q.15 for the equivalent single rise.

Related PYQs

No directly related past PYQ was found.