A shopkeeper sells an item for ₹953.7 after giving two successive discounts of 49% and 75% on its marked price. Had he not given any discount, he would have earned a profit of 10%. What is the cost price (in ₹) of the item?

Correct option is A

Given:

The shopkeeper sells an item for ₹953.7 after giving two successive discounts of 49% and 75% on its marked price.

If no discount were given, the shopkeeper would have earned a 10% profit.

Formula Used:
If two discounts $$d_1$$​  and$$d_2$$​ are applied, the total discount is calculated as:
​$$\text{Final Price} = \text{Marked Price} \times (1 - d_1) \times (1 - d_2)$$​

​$$\text{Selling Price (SP)} = \text{Cost Price (CP)} \times (1 + \text{Profit Percentage})$$​

Solution: ​

Let the marked price be MP .

The selling price after two successive discounts is ₹953.7 

The two discounts are 49% and 75%, so:

​$$\text{Final Price} = MP \times (1 - 0.49) \times (1 - 0.75)$$​

​$$953.7 = MP \times 0.51 \times 0.25$$​

​$$953.7= MP \times 0.1275$$​

​$$MP = Rs. 7480$$​

If no discount were given, the selling price would be equal to the marked price, and the shopkeeper would earn a 10% profit.

​$$\text{Selling Price (SP)} = \text{Cost Price (CP)} \times (1 + \text{Profit Percentage})$$​

​$$7480 = CP \times (1 + 0.1)$$​

​$$7480= CP \times 1.1$$​

​$$CP = Rs. 6800$$​