Question

the present ages of David and Charles are in the ratio 1:2. 9 years from now their ages will be in the ratio 3:5. what is the present age of David​

Answer 1

$\bf{\huge{\underline{\boxed{\rm{\blue{Answer:}}}}}}$

$\bf{\underline{\underline{\sf{\red{Given}}}}}$

• The present ages of David and Charles are in the ratio 1:2
• 9 years from now their ages will be in the ratio 3:5

$\bf{\underline{\underline{\sf{\red{To\:find}}}}}$

• Present age of David

$\bf{\underline{\underline{\sf{\red{Solution}}}}}$

Let x be the common multiple of the ratio 1:2

•°• David's present age = x

Charles's present age = 2x

$\bf{\underline{\underline{\sf{\red{As\:per\:the\:question}}}}}$

Ages after 9 years :-

David's age = x + 9 years

Charles's age = 2x + 9 years

Ratio = 3:5

Representing the condition mathematically,

=> => $\large\frac{x+9}{2x+9}$ = $\large\frac{3}{5}$

Cross multiplying,

=> 5 ( x + 9 ) = 3 ( 2x + 9)

=> 5x + 45 = 6x + 27

=> 5x - 6x = 27 - 45

=> - x = - 18

=> x = 18

Substitute x = 18 in the value of the ratio,

$\bf{\large{\underline{\boxed{\rm{\purple{Present\:age\:of\:David\:=\:x\:=\:18\:years}}}}}}$

$\bf{\large{\underline{\boxed{\rm{\purple{Present\:age\:of\:Charles\:=\:2x\:=\:2\times\:18=\:36\:years}}}}}}$

$\bf\huge\underline{Verification}$

For first case :-

• the present ages of David and Charles are in the ratio 1:2

Present age of David = x = 18 years

Present age of Charles = 2x = 2 × 18 = 36 years

Ratio = 1:2

=> $\large\frac{x}{2x}$ = $\large\frac{1}{2}$

=> $\large\frac{18}{36}$ = $\large\frac{1}{2}$

Dividing LHS by 18,

$\large\frac{1}{2}$ = $\large\frac{1}{2}$

LHS = RHS.

For second case :-

• 9 years from now their ages will be in the ratio 3:5

Ages after 9 years :-

David = x + 9 = 18 + 9 = 27 years

Charles = 2x + 9 = 36 + 9 = 45 years

Ratio = 3:5

=> $\large\frac{x+9}{2x+9}$ = $\large\frac{3}{5}$

=> $\large\frac{27}{44}$ = $\large\frac{3}{5}$

Dividing LHS by 9,

=> $\large\frac{3}{5}$ = $\large\frac{3}{5}$

LHS = RHS.

Hence verified.