​A seller gives two successive discounts of 10% and 20% on a shirt. If the selling price of the shirt is Rs. 720, what is the original marked price?​

Correct option is A

Given:

1. A seller offers two successive discounts of 10% and 20% on the marked price of a shirt.
2. The selling price (SP) of the shirt after these discounts is ₹720.
3. We need to find the original marked price (MP) of the shirt.

Formula Used:

1. Successive Discount Formula:

$$\text{Net Price} = \text{MP} \times (1 - d_1) \times (1 - d_2)$$​​

where $$d_1 , d_2$$ are the first and second discounts, respectively.

2. Selling Price Relation:

\$$\text{SP} = \text{MP} \times (1 - \text{Net Discount Fraction})$$​

Solution:

1. The net price after two successive discounts:

$$\text{Net Price} = \text{MP} \times (1 - 0.1) \times (1 - 0.2)$$​​

Simplify:

$$\text{Net Price} = \text{MP} \times 0.9 \times 0.8$$​​


$$\text{Net Price} = \text{MP} \times 0.72$$​​

2. Given SP = ₹720:

$$720 = \text{MP} \times 0.72$$​​

3. Solve for MP:

$$\text{MP} = \frac{720}{0.72}$$​​


MP = 1000.

Final Answer:

The original marked price of the shirt is ₹1000