Question

The ages of Hari and Harry are in the ratio 5 ratio 7: 4 years from now the ratio of the age will be three : four find the present age

Answer 1

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

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

• The ages of Hari and Harry are in the ratio 5:7
• 4 years from now the ratio of the age will be 3:4

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

• Present age of Hari
• Present age of Harry

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

Let x be the common multiple of the ratio 5:7

•°• Hari's present age = 5x

Harry's present age = 7x

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

Ages after 4 years :-

Hari's age = 5x + 4 years

Harry's age = 7x + 4 years

Ratio = 3:4

Representing the condition mathematically,

=> $\large\frac{5x+4}{7x+4}$ = $\large\frac{3}{4}$

Cross multiplying,

=> 4 (5x + 4) = 3 ( 7x + 4)

=> 20x + 16 = 21x + 12

=> 20x - 21x = 12 - 16

=> - x = - 4

=> x = 4

Substitute x = 4 in the values of the ratio,

$\bf{\large{\underline{\boxed{\rm{\purple{Present\:age\:of\:Hari\:=\:5x\:=\:5\times\:4=\:20\:years}}}}}}$

$\bf{\large{\underline{\boxed{\rm{\purple{Present\:age\:of\:Harry\:=\:7x\:=\:7\times\:4=\:28\:years}}}}}}$

$\bf\huge\underline{Verification}$

For first case :-

• The ages of Hari and Harry are in the ratio 5:7

Present age of Hari = 20 years = x

Present age of Harry = 28 years = y

Ratio = 5:7

=> $\large\frac{x}{y}$ = $\large\frac{5}{7}$

=> => $\large\frac{20}{28}$ = $\large\frac{5}{7}$

Dividing LHS by 4,

=> $\large\frac{5}{7}$ = $\large\frac{5}{7}$

LHS = RHS.

For second case :-

• 4 years from now the ratio of the age will be 3:4

Ages after 4 years :-

Hari = 5x + 4 = 20 + 4 = 24 years

Harry = 7x + 4 = 28 + 4 = 32 years

Ratio = 3:4

=> $\large\frac{5x+4}{7x+4}$ = $\large\frac{3}{4}$

=> $\large\frac{24}{32}$ = $\large\frac{3}{4}$

Dividing LHS by 8,

=> $\large\frac{3}{4}$ = $\large\frac{3}{4}$

LHS = RHS

Hence verified.

Answer 2

Answer:

The present age of Hari = 5x.

The present age of Harry = 7x .

After 4 years .

The Age of Hari = 5x + 4.

The Age of Harry = 7x + 4.

= 5x + 4 = 3

7x + 4. 4

= 4(5x + 4) = 3(7x + 4).

= 20x + 16 = 21x + 12

= 16 - 12 = 21x - 20x

4 = x.

x = 4.

The present age of Hari = 5x .

= 5 × 4

= 20 year's .

The present age of Harry = 7x.

= 7 × 4

= 28 year's .