Question

What is the single equivalent discount to two successive discounts of $20\%$ and $5\%$?

Answer 1

Hint: We start solving the problem by assigning the variable for the printed price. We then find the equivalent price after applying $20\%$ for the printed price. We then apply a $5\%$ discount to the equivalent price we just obtained to find the final price. We then find the total amount of discount attained by subtracting final price and printed price. We then divide this discounted amount with the printed price to get the required answer.

Complete step-by-step answer:
According to the problem, we need to find the single equivalent discount to two successive discounts of $20\%$ and $5\%$.
Let us assume the printed price be ‘p’ and the price we obtain after applying discount for first time be first price and after applying discount for second time be second price.
Let us find the price we obtain after applying a discount of $20\%$ to the price ‘p’.
So, the first price = $\left( 100-20 \right)\%$ of p.
$\Rightarrow $ The first price = $80\%$ of p.
We know that $x\%$ of y is defined as $\dfrac{x}{100}\times y$.
$\Rightarrow $ The first price = $\dfrac{80}{100}\times p$.
$\Rightarrow $ The first price = $0.8p$.
Now, we need to apply $5\%$ to the first price we just calculated to get the final price.
So, the final price = $\left( 100-5 \right)\%$ of 0.8p.
$\Rightarrow $ The final price = $95\%$ of 0.8p.
$\Rightarrow $ The final price = $\dfrac{95}{100}\times 0.8p$.
$\Rightarrow $ The final price = $0.76p$.
Now, let us find the amount that is discounted after applying the discounts.
We know that discounted amount = printed price – final price.
$\Rightarrow $ discounted amount = $p-0.76p$.
$\Rightarrow $ discounted amount = $0.24p$.
We know that the discount percentage is calculated as $\%discount=\dfrac{discounted\ amount}{\operatorname{printed} price}\times 100$.
$\Rightarrow \%discount=\dfrac{0.24p}{p}\times 100$.
$\Rightarrow \%discount=0.24\times 100$.
$\Rightarrow \%discount=24\%$.
So, we have found the single equivalent discount as $24\%$.
∴ The single equivalent discount to two successive discounts of $20\%$ and $5\%$ is $24\%$.

Note: We should not directly add both $20\%$ and $5\%$ to find the single equivalent discount, as it is the wrong way of doing it. We should know that the discount is given on the printed price not on the cost price. We can also calculate the profit if the cost price of the material is mentioned in the problem. Whenever we are asked to solve this type of problem, start applying a discount to the printed price and proceed step-by-step further to get the required result.