A shopkeeper sells an item for ₹960.4 after giving two successive discounts of 30% and 80% on its marked price. Had he notgiven any discount, he would have earned a profit of 40%. What is the cost price (in ₹) of the item?

Correct option is B

Given:

Selling Price after discounts = ₹960.4

Discount 1 = 30%

Discount 2 = 80%

Profit (if no discount) = 40%

Formula Used:

Selling Price = Marked Price $$\times(1 - \frac{\text{Discount1}}{100}) \times (1 - \frac{\text{Discount2}}{100})$$​​

Selling Price (if no discount) = $$\text{Cost Price} \times \left(1 + \frac{\text{Profit \%}}{100}\right)$$​​

Solution:

Let Marked Price be 'M'.

960.4 = M $$\left(1 - \frac{30}{100}\right) \times \left(1 - \frac{80}{100}\right)$$​​

960.4 = M$$\times$$ 0.7$$\times$$ 0.2

960.4 = 0.14M
M = $$\frac{960.4 }{ 0.14}$$​ = ₹6860

Let Cost Price be 'C'.

6860 =$$C \times \left(1 + \frac{40}{100}\right) = 1.4C$$​​

C = $$\frac{6860 }{ 1.4}$$​ = ₹4900

Therefore, the cost price of the item is ₹4900.

Option (B) is right.