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

Solution:

Let the weight of orange= x gm

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

$=x+\frac{8x}{100}\\\\ =\frac{108x}{100}$

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

$x-\frac{10x}{100}\\\\ =\frac{90x}{100}$

Difference between Weight of Grape fruit and Weight of apple

         $=\frac{108 x}{100}-\frac{90x}{100}\\\\ =\frac{18x}{100}$

The percentage by which apple is lighter than the grapefruit=

  $\frac{\text{Difference between Weight of Grape fruit and Weight of apple}}{\text{ Weight of Grape fruit }} \times 100$

      $=\frac{\frac{18x}{100}}{\frac{108x}{100}}\times 100\\\\ \frac{18}{108}\times 100\\\\ =\frac{100}{6}\\\\ =\frac{50}{3}$%

The percentage by which apple is lighter than the grapefruit $=16\frac{2}{3}$%

Answer 2

Answer:

Apple is 16.67% lighter than the grapefruit.

Step-by-step 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,

$\frac{1.08x-0.9x}{1.08x}\times 100$

i.e. $\frac{0.18x}{1.08x}\times 100$

i.e. $0.1667\times 100$

i.e. 16.67%

Hence, apple is 16.67% lighter than the grapefruit.