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
 
 the ages of her sons are
 x = 4
 y = 5