Consider the following Assertion and Reason : Assertion: 15% discount on the marked price of an item is more than the discount of 10% on the marked price of the same item and a subsequent (successive) discount of 5%. Reason: The subsequent (successive) discount is on the discounted amount. Which one of the following is correct with regard to the above Assertion and Reason?
To solve this, we need to compare two scenarios involving discounts on the marked price of an item.
Scenario 1: A single discount of 15% on the marked price.
The formula to calculate the net price after a single discount is: \(\text{Net Price} = \text{Marked Price} \times \left(1 - \frac{\text{Discount \%}}{100}\right)\). Thus, in this scenario: \(\text{Net Price} = \text{Marked Price} \times \left(1 - \frac{15}{100}\right) = \text{Marked Price} \times 0.85\).
Scenario 2: A successive discount of 10% followed by 5%.
In successive discounts, each discount is applied on the price after the previous discount has been applied. Therefore, the formula for the net price after two successive discounts is: \(\text{Net Price} = \text{Marked Price} \times \left(1 - \frac{ \text{First Discount \%}}{100} \right) \times \left(1 - \frac{\text{Second Discount \%}}{100} \right)\). Thus, in this scenario: \(\text{Net Price} = \text{Marked Price} \times \left(1 - \frac{10}{100}\right) \times \left(1 - \frac{5}{100}\right) = \text{Marked Price} \times 0.9 \times 0.95 = \text{Marked Price} \times 0.855\).
By comparing the two scenarios: - Scenario 1 gives: \(\text{Net Price} = \text{Marked Price} \times 0.85\)- Scenario 2 gives: \(\text{Net Price} = \text{Marked Price} \times 0.855\)
Since \(0.85 < 0.855\), Scenario 1 results in a lower net price, meaning the discount in Scenario 1 is greater than in Scenario 2.
This confirms that the Assertion is true.
The Reason states that the subsequent discount is on the discounted amount, which is inherently true in the case of successive discounts. This explains why the second scenario results in a smaller total discount than the first. Therefore, the Reason supports the Assertion.
Conclusion: Both the assertion and the reason are individually true, and the reason is a correct explanation of the assertion.
Important Questions from Discount and MP
If a trader marks the price of an article 50 percent more than the cost price and allows a discount of 30 percent, then what is his profit percentage?
Printed price of a mobile is Rs. 6,400. It is sold in Rs. 2,560 with two consecutive discount. If first discount is 20%, then what is the second discount?
A trader decided to mark his goods 15 percent above the cost price and then offered 40 percent discount. What will be the percentage of profit or loss?
On the sale of 20 percent discount, the value of an item is Rs. 760. What was the real value of the item?
What is the total discount applicable if 3 successive discounts of 20%, 10% and 12.5% are applied?
