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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?


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Solution

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,

=100+8100x=1.08x

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

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

=100-10100x=0.90x

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

Percentage=final-initialinitial×100Percentage=1.08x-0.90x0.90x×100Percentage=0.18x0.90x×100Percentage=0.2×100Percentage=20%

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


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