Question : A shopkeeper offers two successive discounts of 15% and 20% on an article and is still able to earn a 70% profit. If he offers a single discount of 30%, what will his profit percentage be?
Option 1: 70%
Option 2: 75%
Option 3: 65%
Option 4: 50%
Correct Answer: 75%
Solution :
Given,
Successive discounts = 15% and 20%
Profit = 70%
We know,
Selling Price = $\frac{100+\text{Profit%}}{100}\times$ CP, where CP is the cost price.
Let the cost price of an article be Rs. 100
⇒ Price after first discount of 15% = 100 – 15% of 100 = Rs. 85
⇒ Price after second discount of 20% = 85 – 20% of 85 = 85 − 17 = Rs. 68
So, the original cost Price = $\frac{100}{100+70}$ × 68 = $\frac{10}{17}$ × 68 = Rs. 40
To sell the article at a 30% discount,
Selling Price = 100 − $\frac{30}{100}$ × 100 = Rs. 70
⇒ Profit = SP – CP = 70 – 40 = Rs. 30
⇒ Profit Percentage = $\frac{\text{Profit}}{\text{CP}}$ × 100 = $\frac{30}{40}$ × 100 = 75%
Hence, the correct answer is 75%.
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