Question

Find the difference between a discount of 40% and successive discounts of 36% and 4% for Rs 10000.

Answer 1

Hint: Discount of x% on y rupees on an object means the object is being sold for less price. The price reduced is x% of y. The successive discount means if there are two discounts made, the first discount is made on the original price and the second discount is made on the already discounted price. This continues with further discounts too, if made.

Complete step by step answer:
First, we will formulate a formula for calculating a discount of x% on y.
\[Discount = \dfrac{x}{{100}} \times y\]
Now, we will take the case of a 40% discount on Rs 10000.
\[Discount = \dfrac{{40}}{{100}} \times 10000\]
\[ \Rightarrow Discount = 40 \times 100 = 4000..................(i)\]
So, we get the discount as Rs 4000 in the first case.
Now, we will take the second case where two successive discounts are made. The first discount is 36% on the original price of Rs 10000. The second discount of 4% is made on the already discounted price after the first discount.
\[Discount = \dfrac{{36}}{{100}} \times 10000 = 3600.................(ii)\]
Now, the discounted price can be calculated Rs 10,000 - Rs 3,600 =Rs 6,400 .
The second Discount of 4% is made on Rs 6,400.
\[Discount = \dfrac{4}{{100}} \times 6400\]
\[ \Rightarrow Discount = 4 \times 64 = 256.....................(iii)\]
Now, we will add up the two discounts obtained in equation (ii) and equation (iii).
Total Discount =3600+256=3856.
So, we have the values of two discounts. Now, we can calculate the difference.
Difference=4000 - 3856 =144.
So we get a difference of Rs 144.
Hence, the answer is Rs 144.

Note:In the case of a successive discount, we can use a shortcut to find the final discounted price. Suppose, we have successive discounts of x%, y%,z% on original price A.
If the price after the discount is Rs B, then we can use this formula.
\[B = A\left( {1 - \dfrac{x}{{100}}} \right)\left( {1 - \dfrac{y}{{100}}} \right)\left( {1 - \dfrac{z}{{100}}} \right)\]
We can get the total discount by subtracting B from A.
\[Discount = A\left[ {1 - \left( {1 - \dfrac{x}{{100}}} \right)\left( {1 - \dfrac{y}{{100}}} \right)\left( {1 - \dfrac{z}{{100}}} \right)} \right]\]