Question

If Vivyan spends 25% less than Viren, how much percent does Viren spend more than Vivyan?

Answer 1

Hint: First, we have to find $25\%$ of Viren’s amount. So, we will assume Viren’s amount to be 100 as it is easy to calculate with 100. You can take any other number also. Then find $25\%$ of 100. Then how many percent Viren spends more than Vivyan can be given by formula $=\dfrac{decrease\text{ }amount}{original\text{ }amount}\times 100$ . So, we will get the final percentage.

Complete step-by-step solution -
Here, we are given that Vivyan spends $25\%$ less than Viren so we have to assume that Viren has Rs. 100.
So, Viren’s amount $=100$
Now, it is said that Vivyan spends $25\%$ less than Viren so, the formula used to find the amount will be
$25\%$ of 100 can be written as:
$=\left( \dfrac{25}{100}\times 100 \right)=25$
So, subtracting 25 from total amount 100, we get
$=\left( 100-25 \right)=Rs.75$
So, Vivyan spends Rs.75 which is $25\%$ less than Viren’s amount.
So, here the original amount is Rs. 75 and not 100. We will find increase in percentage which is given by
$=\dfrac{decrease\text{ }amount}{original\text{ }amount}\times 100$ where decrease amount is Rs. 25 and original amount will be Rs. 75
So, on substituting these values we will get,
$=\dfrac{25}{75}\times 100=\dfrac{1}{3}\times 100=33.33\%$
So, Viren spends $33.33\%$ more than Vivyan.

Note: Another approach to solving the problem is by taking variable x. Let us assume Viren spends Rs. X.
So, money spent by Vivyan will be 25% less than Viren written as:
$=x-\dfrac{25}{100}\times x=\dfrac{3x}{4}$
Therefore, percentage Viren spends more than Vivyan will be given as:
$=\dfrac{x-\dfrac{3x}{4}}{\left( \dfrac{3x}{4} \right)}\times 100$
$=\dfrac{\left( \dfrac{x}{4} \right)}{\left( \dfrac{3x}{4} \right)}\times 100\Rightarrow \dfrac{100}{3}=33.33%$
So, the answer will be the same but sometimes it becomes difficult to understand by taking variables. So, it is better to assume any number and then to solve it.