Question

the ages in years of Ramesh and Rahim are in the ratio 5 ratio 7 if Ramesh where nine years older and Rahim nine years younger the age of Rahim would have been twice the age of Rahim find their present age​

Answer 1

Answer:

Present age of Ramesh is 15 years and present age of Rahim is 21 years.

Given :

• The ages of Ramesh and Rahim are in the ratio of 5:7.
• If Ramesh was 9 years older and Rahim was 9 years younger , the age of Ramesh would have been twice the age of Rahim.

To find :

• Their ages.

Solution :

Consider,

• Age of Ramesh = 5x
• Age of Rahim = 7x

If Ramesh was 9 years older and Rahim was 9 years younger, the age of Ramesh would have been twice the age of Rahim.

• Ramesh = (5x+9) years
• Rahim = (7x-9) years

According to the question :-

★ Present age of Ramesh = 5×3 = 15 years

★ Present age of Rahim = 7×3 = 21 years

Answer 2

Solution :-

The ages of Ramesh and Rahim are in the ratio 5:7

Therefore,

Let the ages of Ramesh and Rahim be x and y

So,

x/y = 5/7

x = 5y/7. ...eq( 1 )

Now,

According to the question,

The age of Ramesh would be twice the age of Rahim where Ramesh is 9 years older than his present age and Rahim is 9 years younger than his present age.

That is,

x + 9 = 2( y - 9 )

x + 9 = 2y - 18

x - 2y + 27 = 0. ...eq( 2 )

Subsitute eq( 1 ) in eq( 2 ) ,

5y/7 - 2y + 27 = 0

5y/7 - 2y = -27

5y - 14y/7 = -27

5y - 14y = -27 * 7

-9y = -189

y = -189/-9

y = 21

Subsitute the value of y in eq( 1 )

x = 5*21/7

x = 105/7

x = 15

Hence, The present ages of Ramesh and Rahim is 21 years and 15 years $.$