Question

Applied a bill to 15000. What is the difference in rupees between a discount of 50 % and two successive discounts of 30 % and 20 %.

Answer 1

- Hint:In Use the formula, \[\text{Discount}=\dfrac{\left( \text{Discount Percentage} \right)\times \left( \text{List Price} \right)}{100}\] to find the discount in each case. In the first case, the discount % is 50 on Rs.15000 while in the second case, first find a discount of 30 % on Rs. 15000. Find the remaining amount and then find a 20 % discount on it to find the total discount. Here the initial list price is Rs.15000.

Complete step-by-step solution -

In this question, we have to find the difference between a discount of 50 % on Rs. 15000 and two successive discounts of 30 % and 20 % on the same account. First of all, let us see what discount means. Discount is the kind of reduction or deduction in the cost price of the product. The discount rate is given in percentage.
Selling Price = List Price – Discount
\[\text{Discount}=\dfrac{\left( \text{Discount Percentage} \right)\times \left( \text{List Price} \right)}{100}\]
Now, let us consider our question. Let us first find out the value of a discount of 50 % on Rs. 15000. We know that,
\[\text{Discount}=\dfrac{\left( \text{Discount Percentage} \right)\times \left( \text{List Price} \right)}{100}\]
So, we get,
\[\text{Discount}=\dfrac{50\times 15000}{100}\]
= Rs. 7500
So, we get a 50% discount on Rs.15000 means Rs. 7500.
Now, let us find the value of the two successive discounts of 30 % and 20 % on Rs.15000. For this, first, we will find the value of a 30 % discount on Rs. 15000. We know that,
\[\text{Discount}=\dfrac{\left( \text{Discount Percentage} \right)\times \left( \text{List Price} \right)}{100}\]
So, we get,
\[\text{Discount}=\dfrac{30\times 15000}{100}\]
= Rs. 4500
Now, we know that after the discount of Rs. 4500 on Rs. 15000, we get the remaining amount as
Remaining Amount= Rs. 15000 – Rs. 4500 = Rs. 10500
Now, we will find the value of the discount of 20 % on Rs.10500. So, we get,
\[\text{Discount}=\dfrac{20\times 10500}{100}\]
= Rs. 2100
Hence, we get a total discount after two successive discount of 30 % and 20 % on Rs.15000 as,
= Rs. 4500 + Rs. 2100
= Rs. 6600
So, the total discount, in this case, is Rs. 6600
Therefore, we get the difference in discounts in 2 cases = Rs. 7500 – Rs. 6600 = Rs. 900

Note: Students must note that if we are given that there are two successive discounts of a % and b %, we can get the overall percentage by finding the value of \[\left( a+b-\dfrac{ab}{100} \right)\]%. For example, in the above question, the discount of 30 % and 20 % successively means a discount of \[\left( 30+20-\dfrac{30.20}{100} \right)\]% = 44 %. So, now apart from finding two successive discounts of 30 % and 20 % successively, we can directly find a discount of 44 % on Rs. 15000. That is, \[\dfrac{44\times 15000}{100}=6600\] which is the same as what we already calculated. Also, students must not make this mistake of assuming finding two successive discounts of 30 % and 20 % as a discount of 50 %.