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
The marked price of an article is Rs. 1500. A shopkeeper sells it by giving 20% discount on its marked price. If the cost price of the article is Rs. 991, then his profit (in Rs.) is:
Surbhi sold an article for Rs. 176 after giving 12% discount on its marked price. Had she not given any discount; she would have earned a profit of 25%. What is the cost price (in Rs.) of the article?
The marked price of an article is Rs. 240. A shopkeeper sells it by allowing 18% discount on its marked price and still gains 23%. What is the cost price (in Rs.) of the article?
Three shopkeepers A, B and C marked on an identical article at Rs. 4820. A, B and C sold their article on successive discounts of 20% and 20%; 25% and 15%; 30% and 10% respectively. Which shopkeeper gives the maximum discount and how much (in Rs.)?
Find a single discount percentage equivalent to successive discounts of 10%, 20% and 25%.
