Question

Last year, Mr Basu bought two scooters. This year, he sold both of them for Rs 30,000 each. On one scooter, he earned a profit of 20%, and on the other, he made a loss of 20%. What was his net profit or loss?

• A. He gained less than Rs 2000
• B. He gained more than Rs 2000
• C. He lost less than Rs 2000
• D. He lost more than Rs 2000

Hint:

When the same rupee amount is earned by selling one item at a profit and another at an equal percentage loss, the two cost prices are not equal, so work out each cost price separately before comparing totals.

Answer 1

The Correct Option is D

Step 1: Find the cost price of the scooter sold at a profit.
The scooter sold at a 20% profit has a selling price of Rs 30,000. If the cost price is \(C_1\), the selling price equals the cost price plus 20% of the cost price.
\[ 1.2 \times C_1 = 30000 \]
\[ C_1 = \frac{30000}{1.2} = 25000 \]
So this scooter cost Mr Basu Rs 25,000.

Step 2: Find the cost price of the scooter sold at a loss.
The second scooter was sold at a 20% loss, again for Rs 30,000. If its cost price is \(C_2\), the selling price is 80% of the cost price, because a 20% loss means only 80% of the cost is recovered.
\[ 0.8 \times C_2 = 30000 \]
\[ C_2 = \frac{30000}{0.8} = 37500 \]
So this scooter cost Mr Basu Rs 37,500.

Step 3: Find the total cost price and total selling price.
Total cost price \(= C_1 + C_2 = 25000 + 37500 = 62500\).
Total selling price \(= 30000 + 30000 = 60000\).
Since the total cost price is higher than the total selling price, Mr Basu made an overall loss, not a gain.

Step 4: Find the amount of loss.
\[ \text{Loss} = 62500 - 60000 = 2500 \]
A loss of Rs 2500 is more than Rs 2000. This rules out options (A) and (B), which speak of a gain, and also rules out option (C), which says the loss is less than Rs 2000.

Final Answer:
Mr Basu made a net loss of Rs 2500, which is more than Rs 2000. \[ \boxed{\text{He lost more than Rs 2000}} \]