SSC CGL 2024 Tier-I · 19 September 2024, Shift 2 · Quantitative Aptitude · Question 22 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 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.

The price of an item is increased twice successively. The final price is ₹2,295 and initial price was ₹1,000. The percentage increment the second time was twice the percentage increment the first time. By what percentage was the price increased the second time?

(a)70%
(b)65%
(c)35%
(d)25%

Answer

Why

Correct — A. Let the first rise be x%, so the second is 2x%. Successive rises multiply.

1000 × (1 + x/100)(1 + 2x/100) = 2295
(1 + x/100)(1 + 2x/100) = 2.295

Put p = x/100 and expand:
2p² + 3p + 1 = 2.295
400p² + 600p − 259 = 0 (after multiplying by 200)

Discriminant = 600² + 4 × 400 × 259 = 774400, and √774400 = 880
p = (880 − 600) ÷ 800 = 0.35, so x = 35

The second increment is 2x = 70% → option (a)
Check: 1000 → 1350 → 2295, the price the stem gives.

Why the others are wrong

(b)
65% — A second rise of 65% makes the first 32.5%, and 1000 × 1.325 × 1.65 = ₹2,186.25, short of the ₹2,295 the stem fixes.
(c)
35% — 35% is the first increment, not the second. The stem asks for the second, which is twice it — stopping at x is the commonest slip on this question.
(d)
25% — A second rise of 25% makes the first 12.5%, and 1000 × 1.125 × 1.25 = ₹1,406.25, nowhere near ₹2,295.

Concept

Percentages act on the price they find, not on the original. Two rises of a% and b% combine into the single factor (1 + a/100)(1 + b/100), so 35% then 70% is a net rise of 129.5% and not 105%.

The stem also sets its unknown one step back. It describes the second rise through the first, so you solve for the first and then double it.

The quadratic is clean if you clear the decimal early: multiplying 2p² + 3p − 1.295 = 0 by 200 gives whole numbers, and the discriminant 774400 is the perfect square 880².

Key facts

Successive rises multiply: final = initial × (1 + a/100) × (1 + b/100).
A rise of a% followed by b% equals one rise of (a + b + ab/100)%.
Here the net rise is 129.5%, because 2295 is 2.295 times 1000.
35% then 70% takes ₹1,000 to ₹1,350 and then to ₹2,295.

Study next

Successive discounts and the single equivalent discountThe combined-change formula a + b + ab/100 with a negative second termPercentage change measured on a changed base, as in profit after a price revision

Common traps

Adding the two rises into 3x and solving 1000(1 + 3x/100) = 2295.
Answering 35%, the first increment, when the question asks for the second.
Reading twice the percentage as twice the rupee increase.

SSC keeps returning to successive percentage change. On 26 Sep 2024, 09:00, Quant Q.25 it sets two decreases of 25% against two increases of 25% and asks by what percentage one falls below the other.

It also buries the same arithmetic inside profit-and-loss: in this same paper Quant Q.7 works a 5% discount against a 4.5% gain, and Quant Q.9 combines a mark-up with a short weight.

Related PYQs

No directly related past PYQ was found.