SSC CGL 2024 Tier-I · 23 September 2024, Shift 3 · Quantitative Aptitude · Question 21 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 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.

The single discount equivalent to a series discount of 60%, 70% and 80%.

(a)95.5%
(b)85%
(c)70%
(d)97.6%

Answer

Why

Correct — D. Successive discounts multiply the fraction of the price that survives each cut, so put the marked price at ₹100 and apply them in turn.

After 60% off: 100 × 0.40 = ₹40
After 70% off: 40 × 0.30 = ₹12
After 80% off: 12 × 0.20 = ₹2.40

₹2.40 of every ₹100 is still paid, so the discount is
100 − 2.40 = 97.6% → option (d)

As one line of fractions: 0.4 × 0.3 × 0.2 = 0.024, and 1 − 0.024 = 0.976.

Why the others are wrong

(a)
95.5% — 95.5% would leave ₹4.50 payable on ₹100. The three cuts leave 0.4 × 0.3 × 0.2 = 0.024 of the price, which is ₹2.40 — this is the nearest wrong option, and only the product separates it.
(b)
85% — 85% would leave ₹15 payable. But the first two discounts alone already bring ₹100 down to ₹12, before the 80% cut is applied at all.
(c)
70% — 70% is the plain average of 60, 70 and 80. Discounts do not average, because each one acts on the reduced price the previous one left behind.

Concept

A discount of d% leaves (1 − d⁄100) of the price standing. Chain the discounts and you chain the survivors, so the equivalent single discount is 1 minus the product of the surviving fractions.

Here 0.4 × 0.3 × 0.2 = 0.024, so 2.4% of the marked price is still payable and 97.6% has been taken off.

Because it is a product, the order of the three cuts makes no difference to the final price — a useful check if the same cuts are ever listed in a different order.

For two discounts a and b the shortcut a + b − ab⁄100 is faster. Applied here in stages: 60 and 70 give 88, then 88 and 80 give 88 + 80 − 70.4 = 97.6.

Key facts

A d% discount leaves (1 − d⁄100) of the price, so successive discounts multiply.
60%, 70% and 80% in succession leave 0.4 × 0.3 × 0.2 = 0.024 of the marked price.
The single equivalent discount is 100% − 2.4% = 97.6%.
The equivalent of two discounts a% and b% is a + b − ab⁄100 percent.

Study next

The two-discount shortcut a + b − ab⁄100 and its use in stagesSuccessive percentage increases, where the same multiplier chain runs upwardMarked price, selling price and cost price once a single equivalent discount is known

Common traps

Adding the three to 210%, which is impossible for a discount on a positive price.
Averaging them to 70%, an answer that is sitting in the options waiting for you.
Reporting the 2.4% that survives instead of the 97.6% that is taken off.

The numbers here are round, so the whole item is a test of whether you multiply the survivors or add the discounts.

A three-cut series of 15%, 20% and 5% is asked at 25 Sep 2024, 16:00, Quant Q.24 (answer: 35.4%). Choosing the right percentage base also decides Quant Q.15 of this paper, where spending is 40% higher than savings out of an income of ₹72,000.

Related PYQs

No directly related past PYQ was found.

Topic: Discount — all 42 SSC CGL questions on it, every solved shift.