A shopkeeper allows 15% discount on market price of a Table and thus suffered a loss of 10% on it. If he gives 10% discount and wants to make a profit of 40%, then what would be the ratio of his cost price and new market price?a)14:9b)9:14c)17:35d)11:14Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Given information:
- The shopkeeper allows a 15% discount on the market price of a table.
- Due to this discount, the shopkeeper suffers a loss of 10% on the table.
- The shopkeeper now wants to give a 10% discount and make a profit of 40%.

Let's solve the problem step by step:

1. Finding the cost price and market price of the table:
- Let's assume the market price of the table is Rs. 100.
- The shopkeeper allows a 15% discount, so the selling price becomes 85% of the market price.
- Therefore, the selling price is Rs. (85/100) * 100 = Rs. 85.

2. Calculating the loss percentage:
- The shopkeeper suffers a loss of 10% on the selling price, which is Rs. 85.
- The loss amount is 10% of Rs. 85, which is (10/100) * 85 = Rs. 8.5.

3. Determining the cost price:
- The selling price is equal to the cost price minus the loss.
- So, the cost price is Rs. 85 + Rs. 8.5 = Rs. 93.5.

4. Finding the new market price:
- The shopkeeper now wants to give a 10% discount and make a profit of 40%.
- Let's assume the new market price is Rs. 100.
- The shopkeeper gives a 10% discount, so the selling price becomes 90% of the new market price.
- Therefore, the selling price is Rs. (90/100) * 100 = Rs. 90.

5. Calculating the profit percentage:
- The shopkeeper wants to make a profit of 40% on the selling price, which is Rs. 90.
- The profit amount is 40% of Rs. 90, which is (40/100) * 90 = Rs. 36.

6. Determining the new cost price:
- The selling price is equal to the cost price plus the profit.
- So, the cost price is Rs. 90 - Rs. 36 = Rs. 54.

7. Finding the ratio of the cost price and new market price:
- The ratio of the cost price to the new market price is Rs. 54 : Rs. 100.
- Simplifying this ratio, we get 9 : 14.

Therefore, the correct answer is option 'B' - 9:14.

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