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: Recall the net effect rule for equal profit and loss percentages on unequal cost prices.
When two articles are sold at the same selling price, one at a gain of $r\%$ and the other at a loss of $r\%$, there is always a net loss on the whole deal. The overall loss percentage, calculated on the total cost price, works out to $\left(\dfrac{r}{10}\right)^2 \%$. Here $r = 20$.

Step 2: Apply the rule to find the loss percentage.
\[ \text{Loss percent} = \left(\frac{20}{10}\right)^2 = 2^2 = 4\% \]
So Mr Basu's net loss, as a percentage of the total cost price, is 4%.

Step 3: Recover the total cost price from the total selling price.
Total selling price $= 30000 + 30000 = 60000$.
If the loss is 4% of the cost price, the selling price is 96% of the cost price.
\[ 0.96 \times \text{Total CP} = 60000 \]
\[ \text{Total CP} = \frac{60000}{0.96} = 62500 \]

Step 4: Find the actual loss amount and compare with the options.
\[ \text{Loss amount} = \text{Total CP} - \text{Total SP} = 62500 - 60000 = 2500 \]
A loss of Rs 2500 is clearly more than Rs 2000, so any option that mentions a gain, or a loss smaller than Rs 2000, cannot be correct.

Step 5: State the final answer.
Mr Basu's transaction resulted in a net loss of Rs 2500, which is more than Rs 2000. \[ \boxed{\text{He lost more than Rs 2000}} \]