Q.7 A person sold two different items at the same price. He made 10% profit in one
item, and 10% loss in the other item. In selling these two items, the person made a
total of
(A) 1% profit
(B) 2% profit
(C) 1% loss
(D) 2% loss
The person made a 1% loss overall. This occurs because the items share the same selling price, but profit and loss percentages apply to different cost prices. Let the selling price (SP) of each item be 100 units.
Calculation Method
Assume SP = 100 for each item.
- For the 10% profit item: Cost price (CP) = SP / 1.1 = 90.91 units.
- For the 10% loss item: CP = SP / 0.9 = 111.11 units.
- Total CP = 90.91 + 111.11 = 202.02 units.
- Total SP = 100 + 100 = 200 units.
- Net loss = 202.02 – 200 = 2.02 units.
- Loss percentage = (2.02 / 202.02) × 100 ≈ 1%.
General Formula
When two items sell at the same price with x% profit on one and x% loss on the other, net loss = (x/10)² %. Here, x = 10, so loss = (10/10)² = 1%.
Option Analysis
| Option | Explanation |
|---|---|
| (A) 1% profit | Incorrect, as total SP (200) falls short of total CP (202.02). |
| (B) 2% profit | Wrong; no profit occurs due to asymmetric CPs. |
| (C) 1% loss | Correct, matching exact calculation. |
| (D) 2% loss | Too high; actual loss is precisely 1%. |
Correct Answer: (C) 1% loss
Two items same price 10% profit 10% loss scenarios
Two items same price 10% profit 10% loss scenarios often confuse students in profit-loss problems, but they always yield a net loss of 1%. This classic question tests understanding that equal percentage profit and loss on identical selling prices (SP) create unequal cost prices (CP), leading to overall loss.
Why 1% Loss Occurs
Key Insight: Profit % is on lower CP for the profitable item, while loss % is on higher CP for the loss-making item.
Take SP = ₹100 each:
| Item | Profit/Loss | CP Formula | CP (₹) |
|---|---|---|---|
| Item 1 | 10% Profit | 100 / 1.1 | 90.91 |
| Item 2 | 10% Loss | 100 / 0.9 | 111.11 |
- Total CP = ₹202.02
- Total SP = ₹200
- Loss % = [(202.02 – 200) / 202.02] × 100 = 1%
Universal Formula
Net loss % = (x/10)² where x = profit/loss % (here, 10). Proof derives from CP1 = SP/(1 + x/100), CP2 = SP/(1 – x/100).
MCQ Breakdown
- (A) 1% profit: Fails as SP < CP total.
- (B) 2% profit: Ignores CP asymmetry.
- (C) 1% loss: Matches math ✓
- (D) 2% loss: Overestimates by double.
Pro Tip for Exams
Same SP + equal % profit/loss = always loss, never profit or break-even. Practice with x=20% (4% loss) to master.
