Question

If the value of $x\%$ of 75 is given as 12, what will be the value of x?

Answer 1

Hint: We have given that the value of $x\%$ of 75 is 12. We use the fact that $a\%$ of $y = \dfrac{a}{100}\times y$, to start solving the problem. We find the value of ‘x’ by making all the required calculations. Once we find the value of ‘x’, we verify $x\%$ of 75 is coming out to be 12 or not.

Complete step-by-step solution:
Given that the value of $x\%$ of 75 is 12. We need to find the value of x.
We know that a% of y is defined as ‘a’ part per 100 multiplied to y i.e., $a\%$ of y = $\dfrac{a}{100}\times y$.
We have $x\%$ of 75 =12. i.e., $\dfrac{x}{100}\times 75=12$.
We now have $\dfrac{x}{4}\times 3=12$. (as $25\times 3=75$, $25\times 4=100$).
We now have $x\times 3=12\times 4$.
We now have $3x = 48$.
Now, we divide with ‘3’ on both sides.
We now have $\dfrac{3x}{3}=\dfrac{48}{3}$.
We now have $x = 16$.
We got the value of ‘x’ as 16.
Let us verify whether our answer is correct or not.
We need to verify $16\%$ of 75 is 12.
We now have $16\%$ of 75 = $\dfrac{16}{100}\times 75$.
We now have $16\%$ of 75 = $\dfrac{16\times 3}{4}$. (as $25\times 3=75$, $25\times 4=100$).
We now have $16\%$ of 75 = $4\times 3$.
We now have $16\%$ of 75 = 12.
$\therefore$ We verified the value of ‘x’ is 16.

$\therefore$ The value of the variable ‘x’ is 16.

Note: We should not multiply ‘x’ directly with 75, as x is given in percentages. Whenever we see a value of percentage first divide that value with 100. We can also expect problems like finding the factors of ‘x’ after calculating the value of ‘x’.