Question

A girl sells two bags at Rs. 600 each. If she makes a profit of 20% on one of the bags and incurs a loss of 25% on the other, find the resultant gain or loss in the transaction.

• A. Rs. 100 loss
• B. Rs. 200 loss
• C. Rs. 130 gain
• D. Rs. 240 gain

Hint:

When the selling prices are equal but the profit and loss percentages differ, work out each cost price separately and then compare the totals.

Answer 1

The Correct Option is A

Step 1: Convert each percentage into a simple ratio.
For the bag sold at 20% profit, selling price to cost price is in the ratio $120:100$, which simplifies to $6:5$. So cost price is $\frac{5}{6}$ of the selling price.
For the bag sold at 25% loss, selling price to cost price is in the ratio $75:100$, which simplifies to $3:4$. So cost price is $\frac{4}{3}$ of the selling price.

Step 2: Apply the ratios to find each cost price.
\[ CP_1 = 600 \times \frac{5}{6} = 500 \]
\[ CP_2 = 600 \times \frac{4}{3} = 800 \]
These match what a direct percentage calculation would give, confirming the ratio approach works.

Step 3: Add up the cost prices and selling prices separately.
Total cost price $= 500 + 800 = 1300$.
Total selling price $= 600 + 600 = 1200$.

Step 4: Find the difference.
Since cost price exceeds selling price, there is a loss.
\[ \text{Loss} = 1300 - 1200 = 100 \]

Final Answer:
The girl incurs a net loss of Rs. 100 on the whole transaction. \[ \boxed{\text{Rs. 100 loss}} \]