Question

A grapefruit is 8% heavier than an orange, and an apple is 10% lighter than the orange.

By what percentage is the apple lighter than the grapefruit?

Answer 1

Apple is 16.67% lighter than the grapefruit.

Explanation:

Let the weight of the orange = x units

It is given that the weight of grapefruit is 8% heavier than that of the orange.

So, the weight of the grapefruit =
`x+8\%x=x+0.08x=1.08x` units.

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

Then, the weight of the apple=
`x-10\%x=x-0.1x=0.9x` units.

Thus, the percentage by apple is lighter than the grapefruit is,

`(1.08x-0.9x)/(1.08x)* 100`

i.e.
`(0.18x)/(1.08x)* 100`

i.e.
`0.1667* 100`

i.e. 16.67%

Hence, apple is 16.67% lighter than the grapefruit.

Answer 2

Let the weight of orange= x gm

Then , weight of grape fruit= It is 8% heavier than an orange,

`=x+(8x)/(100)\\\\ =(108x)/(100)`

Weight of apple =It is 10% lighter than the orange.

`x-(10x)/(100)\\\\ =(90x)/(100)`

Difference between Weight of Grape fruit and Weight of apple

`=(108 x)/(100)-(90x)/(100)\\\\ =(18x)/(100)`

The percentage by which apple is lighter than the grapefruit=

`\frac{\text{Difference between Weight of Grape fruit and Weight of apple}}{\text{ Weight of Grape fruit }} * 100`

`=((18x)/(100))/((108x)/(100))* 100\\\\ (18)/(108)* 100\\\\ =(100)/(6)\\\\ =(50)/(3)`%

The percentage by which apple is lighter than the grapefruit
`=16(2)/(3)`%