A shopkeeper allow a discount of 10% to his customers and still gains 20%. What is the market price on an article which costs ₹ 450 to the shopkeeper ?

Question

Accepted Answer

To determine the market price of an article that costs ₹ 450 to the shopkeeper, given that he allows a discount of 10% and still gains 20%, we need to follow these steps:

1. **Calculate the Selling Price (SP):**
   - The shopkeeper gains 20% on the cost price (CP) of ₹ 450.
   - Gain = 20% of ₹ 450 = (20/100) × 450 = ₹ 90.
   - Therefore, the Selling Price (SP) = Cost Price (CP) + Gain = ₹ 450 + ₹ 90 = ₹ 540.

2. **Determine the Market Price (MP):**
   - The shopkeeper offers a 10% discount on the Market Price.
   - Let the Market Price be ₹ X.
   - After a 10% discount, the Selling Price is 90% of the Market Price.
   - Therefore, 90% of X = ₹ 540.
   - Solving for X: (90/100) × X = 540
   - X = 540 × (100/90) = 540 × (10/9) = ₹ 600.

Thus, the Market Price of the article is ₹ 600, which corresponds to Option 1.

**Explanation for Incorrect Options:**

- **Option 2 (₹ 540):** This option suggests that the Market Price is equal to the Selling Price, which is incorrect because the Market Price must be higher than the Selling Price to account for the discount.

- **Option 3 (₹ 615):** This option is incorrect because, when calculated, the Market Price required to achieve a Selling Price of ₹ 540 with a 10% discount is ₹ 600, not ₹ 615.

- **Option 4 (₹ 405):** This option is incorrect because it is less than the Cost Price of ₹ 450, which would not allow for any gain, let alone a 20% gain.

Therefore, the correct Market Price, considering the given conditions, is ₹ 600, making Option 1 the correct answer.