Question

What is the difference between a discount of 40 % of Rs. 1000 and two successive discounts of 30 % and 10 % on the same amount?
(a) 0
(b) 20
(c) 30
(d) 40

Answer 1

Hint: Calculate the discount amount of 40 % on Rs. 1000. Then calculate the successive discounts of 30 % and 10 % on the same amount and determine the difference between them. Use the formula for percentage, that is, \[{\text{Percentage}} = \dfrac{{{\text{Required Value}}}}{{{\text{Total Value}}}} \times 100\% \].

Complete step-by-step answer:
Discount is defined as the reduction made in the price of some article. It is expressed as a percentage and can be converted into value.
A percentage is a fraction of an amount expressed as a particular number of hundredths of the amount.

The formula for percentage is given as follows:
\[{\text{Percentage}} = \dfrac{{{\text{Required Value}}}}{{{\text{Total Value}}}} \times 100\% \]
The required value can be calculated if the percentage is given as follows:
\[{\text{Required Value}} = \dfrac{{{\text{Percentage}} \times {\text{Total value}}}}{{100}}...........(1)\]
Using the formula (1), 40 % of Rs. 1000 is given as:
\[40\% of 1000 = \dfrac{{{\text{40}} \times {\text{1000}}}}{{100}}\]
\[40\% of 1000 = Rs.400..............(2)\]

Next, we need to find the successive discount of 30 % and 10 % on Rs. 1000.
We find the discounted price of 30 % on Rs. 1000.
\[30\% of 1000 = \dfrac{{{\text{30}} \times {\text{1000}}}}{{100}}\]
\[30\% of 1000 = Rs.300..........(2)\]
Discounted price = Original price – Discount
Discounted price = 1000 – 300
Discounted price = Rs. 700

Now, we find a discount of 10 % on Rs. 700
\[10\% of 700 = \dfrac{{{\text{10}} \times {\text{700}}}}{{100}}\]
\[10\% of 700 = Rs.300..........(2)\]
Adding equations (2) and (3), the total successive discount of 30 %, and 10 % on Rs. 1000 is Rs. 370.

Hence, from equation (1), we have the required difference:
Difference = 400 – 370
Difference = Rs. 30
Hence, the correct answer is option (c).

Note: The answer is not zero since the discount of 30 % and 10 % on Rs. 1000 is successive and not simultaneous. Hence, you need to calculate the difference by simultaneously applying the discount.