Question

A grapefruit is $8\%$ heavier than an orange, and an apple is $10\%$ lighter than the orange. By what percentage is the grapefruit heavier than the apple?

Answer 1

Finding the percentage by which grapefruit is heavier than apple.

Let the weight of the orange be $x$.

Given, grapefruit is $8\%$ heavier than orange.

This means that the weight of grapefruit can be expressed as,

$$\begin{gathered} =\frac{100+8}{100}x \\ =1.08x \end{gathered}$$

Also, the weight of apple is $10\%$ lighter than orange.

This means that the weight of an apple can be expressed as,

$$\begin{gathered} =\frac{100-10}{100}x \\ =0.90x \end{gathered}$$

Thus, the percent change in the weight of grapefruit as compared to apple is calculated by:

$$\begin{gathered} \text{Percentage}=\frac{\text{final-initial}}{\text{initial}}\times 100 \\ \Rightarrow \text{Percentage}=\frac{1.08x-0.90x}{0.90\left(x\right)}\times 100 \\ \Rightarrow \text{Percentage}=\frac{0.18x}{0.90x}\times 100 \\ \Rightarrow \text{Percentage}=0.2\times 100 \\ \therefore \text{Percentage}=20\% \end{gathered}$$

Hence, the grapefruit is $20\%$ heavier than the apple.