Question

A boy grew one year from a height of c inches to a height of y inches. The percent of increase was
(a) \[\dfrac{100\left( y-x \right)}{y}\]
(b) \[\dfrac{100\left( x-y \right)}{x}\]
(c) \[\dfrac{y-x}{x}\]
(d) \[\dfrac{100\left( y-x \right)}{x}\]
(e) \[\dfrac{x-y}{x}\]

Answer 1

Hint: Height of boy at the beginning and end of year is x and y inches. Now the increase of height in one year is the difference of x and y. Percentage increase is the increase in height by height at beginning multiplied with 100.

Complete step-by-step answer:
Let us take the height of a boy at the beginning of the year as x inches.
We have been told that the height of the boy increased from x inches to y inches in the time period of one year. Hence y inches is the height of the boy at the end of the year.
\[\therefore \] The height increased by the boy in the timespan of one year = y – x.
We are asked to find the percentage increase of the height of the boy.
Percentage increase = (Height increased by the boy in one year / Height of the boy at the beginning of the year) \[\times \] 100.
\[\therefore \] Height increased by the boy = y – x.
Height of boy at the beginning of the year = x.
\[\therefore \] Percentage increase = \[\left( \dfrac{y-x}{x} \right)\times 100\].
\[\therefore \] The percent of increase in height of the boy = \[\dfrac{100\left( y-x \right)}{x}\].
\[\therefore \] Option (d) is the correct answer.

Note: Remember the formula to find the percent increase in the height of the boy. Similarly, there is the formula to find percent decrease, but we don’t want it here as the height can never be reduced, it can be only increased.