​The ratio of the marked price to the cost price of an article is 5 : 3. If the selling price of that article is ₹3645 and the shopkeeper gave two successive discounts of 25% and 10% on the marked price, then what is the profit or loss percent during this transaction?

Correct option is D

Given:

Marked Price (MP) : Cost Price (CP) = 5 : 3

Selling Price (SP) = ₹3645

Discount 1 = 25%

Discount 2 = 10%

Formula Used:

Effective Discount (for successive discounts):

$$\text{Effective Discount} = d_1 + d_2 - \frac{d_1 \times d_2}{100}$$

Where d₁& d₂ are the two successive discounts.

Selling Price (SP):

$$\text{SP} = \left( 1 - \frac{\text{Effective Discount}}{100} \right) \times \text{Marked Price (MP)}$$

Profit or Loss = SP − Cost Price (CP)

$$\text{Profit or Loss Percentage} = \left( \frac{\text{Profit or Loss}}{\text{CP}} \right) \times 100$$

Solution:

 MP : CP = 5 : 3

CP = $$\frac{3}{5}\times$$ MP

Since d₁=25% , d₂= 10%

​Effective Discount = (25 + 10 - $$\frac{25\times 10}{100}$$ )% = 32.5%

Percentage Paid = 100 − 32.5 = 67.5%

Now,   SP = 67.5% of MP

SP = $$\frac{67.5}{100}$$ $$\times$$ MP

MP = $$\frac {3645 \times 100}{67.5}$$ = 5400

So, CP = $$\frac{3}{5}\times$$ 5400 = 3240

Profit = SP − CP = 3645 − 3240 = 405

​$$\text{Profit Percentage} = \left( \frac{\text{Profit }}{\text{CP}} \right) \times 100$$= $$\frac{405}{3240} \times 100=12.5$$%

Thus, option (d) ​profit 12.5% is right answer.​

Effective Discount=d1+d2−d1×d2100\text{Effective Discount} = d_1 + d_2 -