Question

The difference between a discount of 35% and two successive discounts of 20% on a certain bill was 22. Find the amount of the bill.
A) 200
B) 1100
C) 2200
D) 1000

Answer 1

Hint:
We will start by finding the successive discounts of the given percentage of 20% and calculate the total bill amount after the discount. Then we calculate the discount of 35% on the bill amount. Observing their difference, we then use the unitary method to find the amount of the bill.
We begin by letting the total amount of bill to be $x$. We then move forward to find the equivalent amount of the given two successive discounts of 20% and 20% each. Also, note that these discounts are on the bill amount.

Complete step by step solution:
Let us find the bill amount after first 20% discount on the bill amount and we will let the bill amount \[T = 100\] as we have to find the bill amount after 20% discount on the total amount.
$
  A = T\left( {1 - \dfrac{D}{{100}}} \right) \\
   \Rightarrow A = 100\left( {1 - \dfrac{{20}}{{100}}} \right) \\
   \Rightarrow A = {\text{Rs. }}80 \\
 $
Let us find the bill amount after the second 20% discount on the bill amount, which is Rs. 80 now.
\[
  A = T\left( {1 - \dfrac{D}{{100}}} \right) \\
   \Rightarrow A = 80\left( {1 - \dfrac{{20}}{{100}}} \right) \\
   \Rightarrow A = {\text{Rs. 64}} \\
 \]
We now calculate the total amount of the discount after successive discounts.
$
  {\text{ Total Discount}} = 100 - 64 \\
   = {\text{Rs. }}36 \\
 $
Moving further we now calculate the discount of 35% on the total bill amount which is 100.
$
  A = T\left( {1 - \dfrac{D}{{100}}} \right) \\
   \Rightarrow A = 100\left( {1 - \dfrac{{35}}{{100}}} \right) \\
   \Rightarrow A = {\text{Rs. 65}} \\
 $
Now, it is given that the difference between the discount of 35% and two successive discounts of 20 % on the bill amount is 22.
From this we get;
$
  {\text{Rs. 36}} - {\text{Rs. 35}} = {\text{Rs. 36}} \\
   = {\text{Rs. 1}} \\
 $
Now we use the unitary method to find the value of $x$. We note that a difference of Rs. 1 is found on a total bill amount of 100. So, we need to find the value of the $x$, for which the difference is Rs. 22.
By the unitary method, we can get the value of $x$ as when the difference is 1 then the bill amount is 100, so, when the difference is coming as 22 then the bill amount will be as follows:
Thus, we get,
$
  1 \times x = 2200 \\
  x = 2200 \\
 $

Thus, the amount of the bill is Rs. 2200, which is an option (C).

Note:
This type of questions can be solved by using the method of equivalent discounts, as there are two successive discounts involve in the given question. In that case you just need to find the equivalent discounts using the formula, $\left( {A + B - \dfrac{{A \times B}}{{100}}} \right)\% $ and then calculate the direct difference between the obtained value and 35%. Then we apply the unitary method to calculate the total bill amount.