Question

age of Hari and Hariram in the ratio 5 :3. four year from now the ratio of their age will be 3:4 .find the present age​

Answer 1

Question:

Ages of Hari and Hariram are in ratio of 5 : 7. Four years from now the ratio of their ages will be 3:4 . Find their present ages.

Answer:

$\sf{ Let\: us \:consider \:the \:current \:ages\: as : }$

5x and 3x respectively.

$\sf{After \:4 \:years \:the\: ratio \:will\: change\: so \:we\: will\: take :}$

Hari = 5x + 4

Hariram = 7x + 4

$\sf{ Following\: the\: given \:condition : }$

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

Then we will cross multiply the numbers.

$\sf{ (5x + 4 \times 4) (7x +4 \times 3)}$

The product would be :

$\longrightarrow{\sf{ 20x + 16 = 21x + 12}}$

Transposing the like terms give us :

$\longrightarrow{\sf{ 16 - 12 = 21x - 20x }}$

$\implies{\sf{ 4 = x (or) x = 4 }}$

So , we have found the value of x.

$\implies\large\boxed{\sf{ Hari's \:age : 5 \times 4 = 20}}$

$\implies\large\boxed{\sf{ Hariram's\: age: 7\times4 = 28}}$

Answer 2

Answer:

Hari's present age is 20 years.

Hariram's present age is 28 years.

Step-by-step-explanation:

Let the common multiple be x.

From the first condition,

Hari's present age = 5x years

Hariram's present age = 7x years

After four years,

Hari's age = ( 5x + 4 ) years

Hariram's age = ( 7x + 4 ) = years

From the second condition,

$\sf\:\dfrac{5x\:+\:4}{7x\:+\:4}\:=\:\frac{3}{4}\\\\\implies\sf\:4\:(\:5x\:+\:4\:)\:=\:3\:(\:7x\:+\:4\:)\\\\\implies\sf\:20x\:+\:16\:=\:21x\:+\:12\\\\\implies\sf\:16\:-\:12\:=\:21x\:-\:20x\\\\\implies\boxed{\red{\sf\:x\:=\:4}}$

Now,

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

Hariram's present age = 7x = 7 × 4 = 28 years