Question

The difference between a discount of 60 % on Rs. 500 and two successive discounts of 36 % and 4 % on the same amount is ____________.
(a) 0
(b) Rs. 2
(c) Rs. 1.93
(d) Rs. 7.20

Answer 1

Hint: Use the formula, \[\text{Discount = }\dfrac{\left( \text{Discount }\!\!\%\!\!\text{ } \right)\times \left( \text{List Price} \right)}{100}\] to find the discount in each case. In the first case, the discount % is 60 while in the second case, first find the discount of 36 % on Rs. 500. Find the remaining amount and then find a 4 % discount on it to find the total discount.

Complete step by step answer:
In this question, we have to find the difference between a discount of 60 % on Rs. 500 and two successive discounts of 36 % and 4 % 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
\[\text{Discount = }\dfrac{\left( \text{Discount }\!\!\%\!\!\text{ } \right)\times \left( \text{List Price} \right)}{100}\]
Now, let us consider our question. Let us first find out the value of a discount of 60 % on Rs. 500. We know that,
\[\text{Discount = }\dfrac{\left( \text{Discount }\!\!\%\!\!\text{ } \right)\times \left( \text{List Price} \right)}{100}\]
So, we get,
\[\text{Discount = }\dfrac{60\times 500}{100}\]
\[=Rs.300\]
So, we get a 60 % discount on Rs. 500 means Rs. 300.
Now, let us find the value of the two successive discounts of 36 % and 4 % on Rs. 500. For this, first, we will find the value of a 36 % discount on Rs. 500. We know that,
\[\text{Discount = }\dfrac{\left( \text{Discount }\!\!\%\!\!\text{ } \right)\times \left( \text{List Price} \right)}{100}\]
So, we get,
\[\text{Discount = }\dfrac{36\times 500}{100}\]
\[=Rs.180\]
Now, we know that after the discount of Rs. 180 on Rs. 500, we get the remaining amount as
\[\text{Remaining Amount = }500-180=Rs.320\]
Now, we will find the value of the discount of 4 % on Rs. 320. So, we get,
\[\text{Discount = }\dfrac{4\times 320}{100}\]
= Rs. 12.8
Hence, we get a total discount after two successive discount of 36 % and 4 % on Rs. 500
= Rs. 180 + Rs. 12.8
= Rs. 192.8
So, the total discount, in this case, is Rs. 192.8
Therefore, we get the difference in discounts in 2 cases = Rs.. 300 – Rs. 192.8 = Rs. 107.2

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 36 % and 4 % successively means a discount of \[\left( 36+4-\dfrac{36\times 4}{100} \right)%=38.56%\]. So, now apart from finding two successive discounts of 36 % and 4 % successively, we can directly find the discount of 38.56 % on Rs. 500. That is,
\[\dfrac{36.56\times 500}{100}=Rs.192.8\]
which is the same as what we already calculated.