Find the gain percentage, given that Anubha sold her scooter for ₹31524 gaining 1⁄6 th of the selling price.
- (a)30%
- (b)20%
- (c)35%
- (d)5%
Answer
Why
Correct — B. The stem is printed as a picture: find the gain percentage, given that Anubha sold her scooter for ₹31,524, gaining 1⁄6 th of the selling price.
Gain per cent is measured on the cost price, so build the CP first.
Gain = SP⁄6
CP = SP − SP⁄6 = 5SP⁄6
Gain% = (SP⁄6) ÷ (5SP⁄6) × 100 = 1⁄5 × 100 = 20% → option (b)
The SP cancels, so ₹31,524 is never needed. Used anyway it agrees: a gain of ₹5,254 on a cost of ₹26,270 is 20%.
Why the others are wrong
- (a)30% — A gain of 30% on cost is a gain of 30⁄130 = 3⁄13 of the selling price, not 1⁄6. It also puts the cost at 31,524 ÷ 1.3 ≈ ₹24,249.23, not a whole number of rupees.
- (c)35% — A gain of 35% on cost is 35⁄135 = 7⁄27 of the selling price, over a quarter of it. The stem allows 1⁄6, and 7⁄27 ≈ 0.259 against 1⁄6 ≈ 0.167.
- (d)5% — A gain of 5% on cost is only 5⁄105 = 1⁄21 of the selling price. The stem gives away 1⁄6 of it, three and a half times as much.
Concept
Profit and loss percentages are taken on the cost price unless a question says otherwise. This one quotes the gain as a fraction of the selling price, so the fraction has to be re-based before it becomes a percentage.
Put SP = 6 units. The gain is 1 unit, so CP = 5 units and gain% = 1⁄5 = 20%.
In general, if the gain is a fraction f of the SP, then CP = (1 − f) × SP and gain% = f⁄(1 − f) × 100. With f = 1⁄6 that is (1⁄6) ÷ (5⁄6) = 20%.
The ₹31,524 is not needed. Both quantities in the ratio are fractions of the same selling price, so it cancels.
It does check out: gain ₹5,254, cost ₹26,270, and 5,254⁄26,270 = 0.2 exactly. Of the four options, 20% is the one that leaves the cost a whole number of rupees.
Key facts
- Gain per cent is measured on the cost price, so a gain quoted on the selling price must be re-based first.
- If the gain is 1⁄6 of the SP, then CP = 5⁄6 of SP and gain% = (1⁄6) ÷ (5⁄6) = 20%.
- A gain of g% on cost is a gain of g⁄(100 + g) of the selling price, so 20% on cost is 1⁄6 of SP.
- With SP = ₹31,524 the gain is ₹5,254 and the cost is ₹26,270.
Study next
Common traps
- Reading 1⁄6 of the selling price as 1⁄6 of the cost, which gives 16.67% and matches no option.
- Dividing ₹31,524 by 6 and then by ₹31,524 again, which only returns the 1⁄6 you started with.
- Assuming the rupee figure must be used because the question bothered to print it.
12 Sep 2024, 16:00, Quant Q.19 re-bases the other way, with one extra step. The profit is 320% of the cost, then the cost rises by 10% while the selling price stays fixed.
On a cost of 1 the SP is 4.2, the new cost 1.1 and the profit 3.1, so the profit is 3.1⁄4.2 ≈ 73.8% of the selling price.
Quant Q.15 of this paper asks the same job of a household budget, stating spending as 40% above savings out of an income of ₹72,000 and asking for the savings.
Related PYQs
No directly related past PYQ was found.