Explanations:Successive discounts are a common concept in retail pricing and competitive examinations. When a retailer receives successive discounts, the first discount is applied to the original price, and the second discount is applied to the price after the first discount has been applied. This means that the second discount is not applied to the original price but to the reduced price after the first discount.
In this problem, the original price of the calculator is Rs 200. The retailer receives a 10% discount on this price, which reduces the price to 90% of the original price. The calculation for the first discount is:
First discounted price = Original price * (1 - First discount rate)
Substituting the given values:
First discounted price = 200 * (1 - 0.10) = 200 * 0.90 = Rs 180
Next, the retailer receives a second discount on the reduced price of Rs 180. Let the second discount rate be \( x \). The final price after the second discount is given as Rs 153. The calculation for the second discount is:
Final price = First discounted price * (1 - Second discount rate)
Substituting the known values:
153 = 180 * (1 - x)
To find the second discount rate \( x \), we solve the equation:
153 = 180 * (1 - x)
Dividing both sides by 180:
\( \frac{153}{180} = 1 - x \)
Calculating the fraction:
\( 0.85 = 1 - x \)
Solving for \( x \):
\( x = 1 - 0.85 = 0.15 \)
Converting the decimal to a percentage:
\( x = 0.15 \times 100\% = 15\% \)
Therefore, the second discount rate is 15%, which matches the correct answer.
It is important to note that the second discount is applied to the price after the first discount, not to the original price. This is a common misconception that can lead to incorrect calculations. Always ensure that the second discount is applied to the reduced price after the first discount has been applied.