Mrs. Tiwari has two sons, one being exactly one year older than the other. Her age is equal to the sum of the squares of the ages of her sons. If 4 years hence her age becomes five times the age of the elder son then find the ages of her sons.

Let

x = child number 1

y = son number 2

z = Mrs. Tiwari

We have then:

y = x + 1

z = x ^ 2 + y ^ 2

z + 4 = 5 (y+4)

We solve the system:

Equation1

y = x + 1

Equations 1 and 2:

z = x ^ 2 + (x + 1) ^ 2

z = x ^ 2 + x ^ 2 + 2x + 1

z = 2x ^ 2 + 2x + 1

Equation 2 and 3

z + 4 = 5 (y+4)

2x ^ 2 + 2x + 1 + 4 = 5 (x + 1 + 4)

2x ^ 2 + 2x + 5 = 5x + 25

2x ^ 2 + 2x - 5x + 5 - 25 = 0

2x ^ 2-3x - 20 = 0

x = 4

Substituting:

y = x + 1

y = 4 + 1

y = 5

answer:

the ages of her sons are

x = 4

y = 5