Question

Two numbers are in the ratio 3:5. If 8 is added to each number, the ratio becomes 2:3. Find the numbers.​

Answer 1

Given :

Two numbers are in the ratio 3:5. If 8 is added to each number, the ratio becomes 2:3. Find the numbers.

How To Solve :

• Here in this problem we are provided that two numbers have a certain ratio and 8 is added to those numbers after which the ratio becomes 2 : 3. In this case we need to take any variable of our choice, here I have taken x in my solution then we need to add 8. After which we need to simplify it with the new ratio. The result will come with respect to x.

• Secondly, we will put the values of x in the mean terms and get their respective values.

Solution :

Let us assume :

The constant multiple be x

Then,

• The first number be 3x

• The second number be 5x

8 is added to each number :

The number becomes,

• The first number = 3x + 8

• The second number = 5x + 8

New Numbers :

First : Second = 2 : 3

Henceforth, the equation stands :

$\twoheadrightarrow \purple{ \frak{ \frac{ 3x + 8 }{5x + 8} = \frac{2}{3} }}$

By cross multiplying we get

$\twoheadrightarrow \purple{ \frak{ 3(3x + 8) = 2(5x + 8) }}$

Simplifying further....

$\twoheadrightarrow \purple{ \frak{9x + 24 = 10x + 16}}$

Transposing them to the other side of the equation

$\twoheadrightarrow \purple{ \frak{10x - 9x = 24 - 16}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \star \: \underline{ \boxed{ \pink{ \frak{x = 8}}}}$

______________________________

Now, to find the numbers

First Number = 3x = 3 × 8 = 24

Second Number = 5x = 5 × 8 = 40

☞ The first number is 24 whereas the second number is 40