Question

16. The ages of A and B are in the ratio 5:3. After 6 years, their ages will be in the ratio 7:5
The present of A is​

Answer 1

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

The present ages of A and B are 15 years and 9 years respectively.

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

Given :

The Ages of A and B are in ratio = 5 : 3

Ratio of the Ages after 6 years = 7 : 5

To Find :

The present age of A

Solution :

◆ $\textbf{\small{\underline{Consider the Present ages as -}}}$

• A as 5x
• B as 3x

◆ $\textbf{\small{\underline{Ages After 6 Years -}}}$

• A as 5x + 6 = 7
• B as 3x + 6 = 5

★ $\boxed{\sf{\dfrac{5x + 6}{3x + 6} = \dfrac{7}{5}}}$

$\longrightarrow{\sf{\dfrac{5x + 6}{3x + 6} = \dfrac{7}{5}}}$

$\longrightarrow{\sf{5(5x + 6) = 7(3x + 6)}}$

$\longrightarrow{\sf{25x + 30} = 21x + 42}$

$\longrightarrow{\sf{25x - 21x= 42 - 30}}$

$\longrightarrow{\sf{4x= 12}}$

$\longrightarrow{\sf{x = \dfrac{12}{4}}}$

$\longrightarrow{\sf{x = 3}}$

$\rule{300}{1.5}$

★ Value of 5x

$\longrightarrow$ 5 × 3

$\longrightarrow$ 15

A is 15 years old

$\rule{300}{1.5}$

★ Value of 3x

$\longrightarrow$ 3 × 3

$\longrightarrow$ 9

B is 9 years old.

$\therefore$ The present ages of A and B are 15 years and 9 years respectively.

$\rule{300}{1.5}$

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

Check if the ratio of their present ages is 5 : 3 and age after 6 years is 7 : 5 or not.

◆ $\textbf{\small{\underline{Present ages -}}}$

• A is 15
• B is 9

◆ $\textbf{\small{\underline{After 6 years -}}}$

• A is 15 + 6 = 21
• B is 9 + 6 = 15

◆ $\textbf{\small{\underline{Present age Ratio -}}}$

$\longrightarrow{\sf{\dfrac{15 \div 3}{9 \div 3}} = \dfrac{5}{3} = 5 : 3}$

◆ $\textbf{\small{\underline{Ratio of ages after 6 years -}}}$

$\longrightarrow{\sf{ \dfrac{21 \div 3}{9 \div 3}} = \dfrac{7}{3} = 7 : 3}$

$\therefore$ The present ages of A and B are 15 years and 9 years respectively.

Answer 2

Let the present age of A and B be as 5x and 3x

==> (5x + 6)/(3x + 6) = 7/5

==> 5(5x + 6) = 7(3x + 6)

==> 25x + 30 = 21x + 42

==> 25x - 21x = 42 - 30

==> 4x = 12

==> x = 3

>> 5x = 5 × 3 = 15

Present age of A is 15 years.

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