Question

What percentage of 75 is 112.5?

Answer 1

Hint: We will first assume that 75 is 100% since it is our output value. Then we will assume the value we seek as x that is 112.5 is x%. Then we will divide both to get the answer.
Complete step-by-step answer:
Before proceeding with the question, we should understand the concept of percentage.
A percent is a number that represents the fractional part out of 100 (per cent literally means per one hundred). It is often denoted using the percent sign, "%". Percentage is a dimensionless number (pure number). Example- 94% means ​ \[\dfrac{94}{100}\]. Likewise, we can represent a denominator of 100 with decimals by moving the decimal point by 2 places. So \[94\times \dfrac{1}{100}=0.94\]. Thus \[94\%=0.94=\dfrac{94}{100}\].
Now assuming 75 is 100% as it is the output value. We will assume x as the percentage of 75 which will be 112.5 .
So using this information we get,
\[100\%=75........(1)\]
\[x\%=112.5........(2)\]
Now by simply dividing equation (1) by equation (2) and taking note of the fact that both the left hand side (LHS) of both equations have the same unit %, so using this information we get,
\[\dfrac{100\%}{x\%}=\dfrac{75}{112.5}.......(3)\]
Now cancelling terms and cross multiplying the terms on both sides, we get,
\[x=\dfrac{112.5\times 100}{75}.......(4)\]
Now solving for x in equation (4) we get,
\[x=150\%\]
Therefore 112.5 is 150% of 75.

Note: Here in this type of question we have to remember how to convert one number with respect to another number into percentage and we also have to keep in mind that ‘’of” means multiplication. We may get confused in reading the question seeing ‘’of” so we need to be clear with the basic concepts.