SSC CGL 2024 Tier-I · 25 September 2024, Shift 1 · Quantitative Aptitude · Question 8 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.

Ramesh purchased 130 books at the rate of ₹200 each and sold half of them at the rate of ₹300 each, one-fifth of them at the rate of ₹350 each and the rest at the cost price. Find his profit percentage.

Answer

Why

Correct — B. Fix the cost first, then split the 130 books into the three lots the stem describes.

Cost price = 130 × ₹200 = ₹26,000

Half of 130 = 65 books at ₹300 = ₹19,500
One-fifth of 130 = 26 books at ₹350 = ₹9,100
Rest = 130 − 65 − 26 = 39 books at ₹200 = ₹7,800

Total selling price = 19,500 + 9,100 + 7,800 = ₹36,400
Profit = 36,400 − 26,000 = ₹10,400
Profit % = 10,400⁄26,000 × 100 = 40%

40% is option (b).

Why the others are wrong

(a)
Option (a), 44%, needs a profit of ₹11,440 on the ₹26,000 cost. The three lots bring in ₹36,400 in all, so the gain is ₹10,400 and no lot is priced high enough to close the ₹1,040 gap.
(c)
Option (c), 35%, is exactly what you get by selling the one-fifth lot at ₹300 as well: 19,500 + 7,800 + 7,800 = ₹35,100, a profit of ₹9,100 on ₹26,000.
(d)
Option (d), 38%, needs a profit of ₹9,880. The stem's own prices produce ₹10,400, so this lands between the 35% and 40% figures without matching either.

Concept

Profit percentage is always profit ÷ cost price × 100, never profit over selling price. Here the cost is fixed once, at ₹26,000 for all 130 books.

The lot sold at cost price is not decoration. Those 39 books add ₹7,800 to both the cost and the selling price, so they contribute nothing to the profit while still sitting in the denominator.

Both fractions are taken of the whole 130, not of what is left after the previous lot: half is 65, one-fifth is 26, and the remainder is what those two leave.

The stem prices the last lot at the cost price, ₹200, without naming the figure again. That is the number you have to carry forward from the opening line.

Key facts

The lot costs 130 × ₹200 = ₹26,000.
The three lots are 65 books at ₹300, 26 books at ₹350 and 39 books at ₹200.
Total selling price is ₹36,400, so the profit is ₹10,400.
₹10,400 on a cost of ₹26,000 is a profit of 40%.

Study next

Profit percentage when one purchase is sold in lots at different ratesMarkup followed by a discount on the same articleFalse-weight problems, where the effective cost price is what shifts

Common traps

Taking one-fifth of the 65 books left after the half, instead of one-fifth of all 130.
Leaving the 39 cost-price books out of the selling price, which drops the profit to ₹2,600.
Dividing the profit by the selling price, which gives 28.6% and matches no option.

SSC splits one purchase into fractional lots and prices each separately, so the item turns on getting the third lot's count right. Profit and loss percentage returns in different clothing at Quant Q.11 of this shift, at 13 Sep 2024, 12:30, Quant Q.16 and at 26 Sep 2024, 12:30, Quant Q.11.

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