Question

The difference between the discounts of 40% on Rs. 500 and two successive discounts of 36% and 4% on the same price is-
A. Rs. 2
B. Rs. 7.20
C. Rs. 1.93
D. Rs. 7

Answer 1

Hint: This problem requires the concept of percentages and profit-loss. We will first find the discounted amount for 40%. Then we will find the successive discount rates of 36% and 4%. We will then subtract these discounted rates to find the answer. The discounted rate of x% discount on an amount of Rs. A can be calculated as-
$D\; = A - x\% \;of\;A$

Complete step-by-step answer:

We have been given an amount of Rs. 500, so we will first calculate the discounted amount of 40% discount. This can be calculated as-
$\begin{align}
  &D = A - x\% \;of\;A \\
  &D = 500 - 40\% of500 \\
  &D = 500 - \dfrac{{40}}{{100}} \times 500 \\
  &D = 500 - 40 \times 5 = 500 - 200 \\
  &D = Rs.\;300 \\
\end{align} $
Now, we will find the successive discounted price of 36% and 4%. So, first we will find the price after a discount of 36%. This can be calculated as-
$\begin{align}
  &{D_1} = 500 - 36\% of500 \\
  &{D_1} = 500 - \dfrac{{36}}{{100}} \times 500 \\
  &{D_1} = 500 - 36 \times 5 = 500 - 180 \\
  &{D_1} = Rs.\;320 \\
\end{align} $
Now, we will find the discounted price of 4% on this amount of Rs. 320. This can be calculated as-
$\begin{align}
  &{D_2} = 320 - 4\% \;of\;320 \\
  &{D_2} = 320 - \dfrac{4}{{100}} \times 320 \\
  &{D_2} = 320 - 4 \times 3.2 = 320 - 12.8 \\
  &{D_2} = Rs.\;307.2 \\
\end{align} $
We have now computed the discounted price of 40% and successive discounted prices of 36% and 4%. Finally, we just have to subtract these two prices so that we can get the final answer. This can be done as-
$\begin{align}
  &Difference = {D_2} - D \\
  &Difference = Rs.\;307.2 - 300 \\
  &Difference = Rs.\;7.20 \\
\end{align} $
This is the final answer, the correct option is B.

Note: Students often think that the difference should be 0, because the same amount of discount is being applied to the initial amount. But as we can see, the final discounts vary slightly, by about Rs. 7. This happens because in the second case, the discount of 4% is being applied to an amount of Rs. 320, and not Rs. 500. This slight change brings a slight difference in the discounted amounts.