Question

two numbers are such that the ratio between them is 3:5 if each is increased by 5 the ratio between the new number so formed is 2: 3 find the other number​

Answer 1

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

The Numbers are 15 and 25.

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

Given :

Ratio of the Numbers = 3 : 5

When increased by 5 new ratio = 2 : 3

To Find :

The Original Numbers

Solution :

◆ $\textbf{\small{\underline{Consider the -}}}$

• One Number as 3x
• Second Number as 5x

$\rule{300}{1.5}$

◆ $\textbf{\small{\underline{According to the Question -}}}$

• 3x + 5 = 2
• 5x + 5 = 3

★ $\boxed{ \frac{(3x + 5)}{(5x + 5)} = \frac{2}{3}}$

$\longrightarrow \: \dfrac{(3x + 5)}{(5x + 5)} = \dfrac{2}{3}$

$\longrightarrow \: \dfrac{3x + 5}{5x + 5} = \dfrac{2}{3}$

$\longrightarrow \: 3(3x + 5) = 2(5x + 5)$

$\longrightarrow \:9x + 15 = 10x + 10$

$\longrightarrow \:9x - 10x = 10 - 15$

$\longrightarrow \:\cancel - x = \cancel - 5$

$\rule{300}{1.5}$

★ Value of 3x

$\longrightarrow \:3 \times 5$

$\longrightarrow \:15$

One Number = 15

$\rule{300}{1.5}$

★ Value of 5x

$\longrightarrow \:5 \times 5$

$\longrightarrow \:25$

Second Number = 25

$\therefore$ The Numbers are 15 and 25.

$\rule{300}{1.5}$

$\mathfrak{\large{\underline{\underline{Verification :-}}}}$

$\longrightarrow \: \dfrac{15 + 5}{25 + 5} = \dfrac{2}{3}$

$\longrightarrow \: \dfrac{20}{30} = \dfrac{2}{3}$

$\longrightarrow \: \dfrac{20 \div 10}{30 \div 3} = \dfrac{2}{3}$

$\longrightarrow \: \dfrac{2}{3} = \dfrac{2}{3}$

$\therefore$ The Numbers are 15 and 25.

Answer 2

Let the original number be x and y.

Given

x : y = 3 : 5   ...( i )

Also, x + 5 : y + 5 = 2 : 3   ...( ii )

From the first equation we get,

==> x/y = 3/5

==> x = 3y/5

Substituting this in the second equation we get,

⇒ ( 3y/5 ) + 5 / y + 5 = 2 / 3

Cross multiplying -

==> 3 [ (3y/5 ) + 5 ] = 2 ( y + 5 )

==> 9y/5 + 15 = 2y + 10

==> 2y - 9y/5 = 15 - 10

==> ( 10y - 9y ) / 5 = 5

==> y/5 = 5

==> y = 25

Therefore x is :

==> x = 3y/5

==> x = ( 3 × 25 ) / 5

==> x = 75/5 = 15

.°. The original numbers were 15 and 25.