Question

The present age ratio between hari& Harry is 5:7. After four years ago these age ratio is 3:4.find these present ages.

Answer 1

Correct Question :-

The present age ratio of between Hari and Harry is 5 : 7. After 4 years the ratio of their ages will be 3 : 4. Find their present ages.

Solution :-

Let :-

Present age of Hari = x

Present age of Harry = y

Four years ago :-

Age of Hari = x - 4

Age of Harry =  y - 4

According to the first condition :-

$\longrightarrow \sf \dfrac{x}{y} = \dfrac{5}{7} \\\\\longrightarrow x = \dfrac{5}{7} y \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ................(1)$

According to the second condition :-

$\longrightarrow \sf \dfrac{x+4}{y+4}= \dfrac{3}{4} \\\\\longrightarrow 4(x+4) = 3(y+4) \\\\\longrightarrow 4x+16 = 3y+12 \\\\\longrightarrow 4x-3y = 12-16 \\\\\longrightarrow 4x-3y = -4 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ................(2)$

Substitute the value of x in eq (2) :-

$\longrightarrow \sf 4 \times \dfrac{5}{7}y -3y = -4 \\\\\longrightarrow \dfrac{20y-21y} {7}= -4 \\\\\longrightarrow -y = -28 \\\\\longrightarrow \bf y = 28$

Substitute y = 28 in eq (1) :-

$\longrightarrow \sf x = \dfrac{5}{7} \times 28 \\\\\longrightarrow x = 5 \times 4 \\\\\longrightarrow \bf x = 20$

Present age of Hari  = 20 years

Present age of Harry = 28 years

Answer 2

✦ Question

The present age ratio of between Hari and Harry is 5 : 7. After 4 years the ratio of their ages will be 3 : 4. Find their present ages.

✦ Given

The present age ratio of between Hari and Harry is 5 : 7. After 4 years the ratio of their ages will be 3 : 4.

✦ To Find

What's their present ages ?

✦ Solution

Ages of Hari and Harry are in the ratio = 5:7

Ratio of ages of Hari and Harry after 4 years = 3:4

Consider Hari present age = 5x years

Harry present age = 7x years

Four years later, Hari age = ( 5x + 4 ) years

Harry age = ( 7x + 4 ) years

As per the Question ,

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

By cross multiplication, we have

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

= 20x + 16 = 21x + 12

= 16 - 12 = 21x - 20x

4 = x

Hence ,

Hari's present age = 5x years = ( 5 × 4 ) years = 20 years.

Harry's present age = 7x years = ( 7 × 4 ) years = 28 years.