An article costs₹1,000 for a salesman. He fixes its marked price as₹1,500. He sells it to a customer at a discount of 20%. He gives a furtherdiscount of 10% for each cash payment. Find the percentage of loss or gain that the salesman makes on sale.
- (a)loss 10%
- (b)gain 10%
- (c)loss 8%
- (d)gain 8%
Answer
Why
Correct — D. Apply the two discounts to the marked price one after the other, then compare with the cost.
Marked price = ₹1,500
After 20%: 1500 × 0.80 = ₹1,200
After a further 10%: 1200 × 0.90 = ₹1,080
Selling price ₹1,080 against a cost of ₹1,000, so profit = 1080 − 1000 = ₹80.
Profit % = 80 ⁄ 1000 × 100 = 8%, and it is a gain → option (d).
Why the others are wrong
- (a)loss 10% — A loss needs the selling price to fall below the ₹1,000 cost, but ₹1,080 is above it. The 10% in the question is the second discount, charged on ₹1,200, not a loss on cost.
- (b)gain 10% — A 10% gain would mean selling at ₹1,100. The discounts leave ₹1,080, because the second one is taken on the already-reduced ₹1,200 rather than on ₹1,500.
- (c)loss 8% — The size is right and the direction is wrong. ₹1,080 exceeds ₹1,000, so the 8% is a gain — subtract cost from selling price before naming the sign.
Concept
Two discounts in succession do not add. The second is charged on what survives the first, so 20% then 10% is a multiplier of 0.80 × 0.90 = 0.72, not a single 30%.
Here 1500 × 0.72 = ₹1,080, and that is the selling price.
Profit or loss is then measured against the cost price and never against the marked price: profit % = (SP − CP) ⁄ CP × 100 = 80 ⁄ 1000 × 100.
Marked price, discount and cost price are three separate anchors, and each percentage in the question is charged on a different one — that is what makes the item worth its 2 marks rather than its arithmetic.
The single equivalent discount of 20% and 10% is 28%, not 30%, which is a useful shortcut when the numbers are less friendly than these.
Key facts
- Successive discounts of a% and b% are equivalent to a single discount of a + b − ab ⁄ 100.
- A 20% discount followed by a 10% discount equals one discount of 28%.
- Profit percentage is always taken on the cost price, never on the marked price or the selling price.
Study next
Common traps
- Adding the discounts to 30%, selling at ₹1,050, and reporting a 5% gain.
- Taking the profit percentage on ₹1,080 instead of on the ₹1,000 cost.
- Reading 8% as a loss because the option list offers both signs at the same size.
SSC reuses this chain with the anchors moved around — sometimes the selling price is asked, sometimes the profit percentage, sometimes the missing discount.
A two-discount version is set at 17 Sep 2024, 16:00, Quant Q.23 and a three-discount version at 19 Sep 2024, 16:00, Quant Q.20.
Related PYQs
No directly related past PYQ was found.