Question

The ratio of two no is 7:5 and the difference of the square of the no. Is 96 find the no.

Answer 1

Let the unit ofvration be a.Then,the numbers will beb7a and 8a

A/c
=>(7a)^2 - (5a)^2 = 96
=>49a^2 - 25a^2 = 96
=>24a^2 = 96
=>a^2 = 96/24
=>a^2 = 4
=>a = 2

Hence, the numbers are 7×2=14 and 5×2=10.

Answer 2

Given:

The ratio of two no is 7:5 and the difference of the square of the no. is 96.

To find:

The numbers.

Solution:

The two numbers are 14 and 10.

To answer this question, we will follow the following steps:

As given, we have,

The ratio of two numbers = 7:5

Let the common ratio be x.

So,

One number = 7x

The second number = 5x

Now,

The difference of the square of the numbers = 96

So,

${(7x)}^{2} - {(5x)}^{2} = 96$

On solving the above, we get

$49 {x}^{2} - {25x}^{2} = 96$

$24 {x}^{2} = 96$

${x}^{2} = 4$

$x = + 2 \: and \: - 2$

On putting x = 2,

The one number = 7x = 7(2) = 14

The second number = 5x = 5(2) = 10

Hence, the two numbers are 14 and 10.