Question

After getting two successive discounts, a pressure cooker with a list price of ₹1500 is available at ₹1050. If the second discount is 12.5%, then the first discount (in %) is:

• A. 15
• B. 20
• C. 22
• D. 34

Hint:

To simplify calculations with 12.5%, remember that $12.5\% = \frac{1}{8}$. A 12.5% discount means the price becomes $\frac{7}{8}$ of the previous value.

Answer 1

The Correct Option is B

Concept: Successive discounts are applied one after the other on the remaining value. If the list price is $L$, the first discount is $d_1\%$, and the second is $d_2\%$, the final price $S$ is calculated as: \[ S = L \times \left(1 - \frac{d_1}{100}\right) \times \left(1 - \frac{d_2}{100}\right) \]

Step 1: Calculate the price after the first discount.
Let the price after the first discount be $P$. We know that after a 12.5% discount on $P$, the final price is ₹1050. \[ P \times \left(1 - \frac{12.5}{100}\right) = 1050 \] \[ P \times \left(\frac{87.5}{100}\right) = 1050 \] \[ P = \frac{1050 \times 100}{87.5} = \frac{105000}{87.5} = ₹1200 \]

Step 2: Calculate the first discount percentage.
The list price was ₹1500 and it was reduced to ₹1200 after the first discount. Amount of first discount $= 1500 - 1200 = ₹300$. \[ \text{First Discount \%} = \left(\frac{300}{1500}\right) \times 100 = \frac{1}{5} \times 100 = 20\% \]