What price should Suneeta marked on a Saree which costs Rs. 2,200 so as to gain 26% after allowing a discount of 12%?

Question

Accepted Answer

To determine the marked price on the saree that allows Suneeta to gain a 26% profit after giving a 12% discount, we need to follow these steps:

1. **Calculate the Selling Price for a 26% Gain:**
   - The cost price of the saree is Rs. 2,200.
   - To gain 26%, the selling price (SP) should be:
     $$
     \text{SP} = \text{Cost Price} + \text{Profit}
     $$
     $$
     \text{Profit} = 26\% \text{ of Cost Price} = \frac{26}{100} \times 2200 = 572
     $$
     $$
     \text{SP} = 2200 + 572 = 2772
     $$

2. **Determine the Marked Price (MP) with a 12% Discount:**
   - Let the marked price be $ x $.
   - After a 12% discount, the selling price should still be Rs. 2,772.
   - The selling price after discount is given by:
     $$
     \text{SP} = x - \left(\frac{12}{100} \times x\right) = 0.88x
     $$
   - Set this equal to the required selling price:
     $$
     0.88x = 2772
     $$
   - Solve for $ x $:
     $$
     x = \frac{2772}{0.88} = 3150
     $$

Thus, the marked price should be Rs. 3,150 to achieve a 26% gain after allowing a 12% discount. Therefore, Option 3 is correct.

**Explanation for Incorrect Options:**

- **Option 1: Rs. 3,050**
  - If the marked price were Rs. 3,050, the selling price after a 12% discount would be:
    $$
    \text{SP} = 3050 \times 0.88 = 2684
    $$
  - This selling price does not provide a 26% gain on the cost price of Rs. 2,200, as it is less than Rs. 2,772.

- **Option 2: Rs. 3,075**
  - If the marked price were Rs. 3,075, the selling price after a 12% discount would be:
    $$
    \text{SP} = 3075 \times 0.88 = 2706
    $$
  - This selling price is also less than the required Rs. 2,772 for a 26% gain.

- **Option 4: Rs. 3,175**
  - If the marked price were Rs. 3,175, the selling price after a 12% discount would be:
    $$
    \text{SP} = 3175 \times 0.88 = 2794
    $$
  - This selling price exceeds the required Rs. 2,772, indicating a higher gain than 26%.

Therefore, only Option 3, Rs. 3,150, results in the correct selling price of Rs. 2,772, ensuring a 26% gain after a 12% discount.