Question

What is the number which when increased by $15\% $ becomes $414$.

Answer 1

Hint: Here we are asked to find the number which when increased by $15\% $ becomes $414$. So, we will have to decrease the number $414$ by $15\% $ so as to get the required number. The number $414$is subtracted by $15\% $ to get the final answer.

Complete step by step answer:
Let us consider the number which is to be found as $x$. So according to the condition given in question i.e., the number which when increased by $15\% $ becomes $414$. Forming the equation of the above condition:
$x + 15\% x = 414$
We will calculate the simplified form of $15\% $
$\because 15\% = \dfrac{{15}}{{100}} = 0.15$
Substituting this value of percentage in the equation
\[x + 0.15x = 414\]
Solving this equation to find the value of $x$ .
$1.15x = 414$
$\Rightarrow x = \dfrac{{414}}{{1.15}}$
$\therefore x = 360$

Therefore, the number which when increased by $15\% $ becomes $414$ is $360$.

Note: A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by whole and multiply by 100.Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”. Percentages have no dimension, hence are dimensionless numbers.