Question

The present age of Kavya's mother is four times that of Kavya'age . Ten years from now , kavya's age will be half of her mother's age . What are their present ages?

Answer 1

Let the present age of kavya is x and mother's age =4x

From ten years now,

Age of kavya =y and age of mother =2y

Converting in equation,

x+10=y. ----------1equation multiply by 4
4x+10=2y. ---------2equation multiply by 1

4x+40=4y
4x+10=2y

Subtract both the equations

30=2y

15=y

Then

After 10 years kavya age will be 15 and Mother age will be 30

Present age of kavya =15-10=5 years

Present age of mother =4*5=20years

I hope this much will help you

Answer 2

let the present age of her mother be x
and kavya's age be y
ATP
x = 4y --------------------- ( 1 )
after 10 yrs , her mother's age will be 10+x
and her age will be 10+y

ATP
10 + y = 10+x / 2
2 (10+y) = 10+x
20 + 2y = 10+4y (x = 4y )
20 - 10 = 4y -2y
10 = 2y

y = 5
present age of kavya is 5 yrs
and her mother age is 5 × 4 = 20years