Question

The ratio of ages today of Vinayak and Manish is 10:9. eight years ago the ratio of their ages then was 6:5. Find their ages today.​

Answer 1

Let x and y be their present ages respectively

As per question

x:y= 10:9

x/y=10/9

x= 10y/9 (1)

8 years ago, their ages were

x-8 and y-8

x-8:y-8= 6:5

x-8/ y-8 = 6/5

5(x-8)= 6(y-8)

Putting the value of x

5(10y/9 -8)= 6y-48

5(10y-72)/9= 6y-48

50y-360= 54y-432

54y-50y= 432-360

4y= 72

y= 72/4= 18

therefore x= 10×18/9 = 10×2= 20

Their present ages are Vinayak = 20years

and Manish= 18 years

Or simply in one variable

let 10x and 9x be their ages respectively

As per question

10x-8/9x-8= 6/5

5(10x-8)= 6(9x-8)

50x-40=54x-48

4x=8

x=2

Vinayak= 10x= 10×2= 20

Manish= 9x= 9×2= 18