Question

What percent of 150 is 114?

Answer 1

Hint: To calculate what percent of 150 is 114, we should use the definition of percentage, i.e., specific kind of values per 100 values. Then, we will need to use the technique of unitary method to find the required value. From a set of 150 values, we are interested in 114 of them. So, from 100 values, we will need $\dfrac{114}{150}\times 100$. Hence, we will get the required answer.

Complete step-by-step answer:
We know very well that the word ‘percentage’ is made up of a combination of 2 words, ‘per’, which means ‘for every’, and ‘cent’, which is equivalent to the number 100. Hence, we can clearly say that, percentage refers to the number of specific values per hundred values.
In our given problem, we need to find what percent of 150 is 114.
Let us assume $x\%$ of 150 is 114.
According to the definition of percentage, $x$% means $x$ out of 100.
So, we can rephrase this as,
From 100, we need = $x$.
So, using unitary method, we can say that
From 1, we need = $\dfrac{x}{100}$
And thus,
From 150, we need = \[\dfrac{x}{100}\times 150\].
Thus, we now have,
\[\dfrac{x}{100}\times 150=114\]
On simplifying, we can get
\[\dfrac{x}{100}=\dfrac{114}{150}\]
And thus,
\[x=\dfrac{114}{150}\times 100\]
$\Rightarrow x=\dfrac{114}{3}\times 2$
$\Rightarrow x=76$
Thus, we get that 76 % of 150 is 114.

Note: We should understand the concepts of unitary method to solve this problem. Alternatively, we can use the direct formula to solve this problem, which can be written as, A% of B = $\dfrac{A}{100}\times B$. Thus, we get $\left( \dfrac{114}{150}\times 100 \right)\%$.