Question

10 years ago, a woman was thrice the age of her daughter. Two years later her daughter’s age will be 30 more than the age of the mother. What are the present ages of the woman and the daughter?

(a) 70 years, 40 years

(b) 60 years, 40 years

(c) 55 years, 25 years

(d) 45 years, 20 years

I got this question in an online interview.

This is a very interesting question from Solution of Two Linear Equations in Two Variables in Different Methods in division Pair of Linear Equations in Two Variables of Mathematics – Class 10

Answer 1

Correct option is (c) 55 years, 25 years

The best explanation: Let the present ages of mother be x years and daughter be y years.

10 years ago,

Age of mother = x-10 years

Age of daughter = y-10 years

Age of mother = 3(age of daughter)

x-10=3(y-10)

x-10=3y-30

x-3y+20=0

x=3y-20     (1)

Two years later,

Age of mother = x+2 years

Age of daughter = y+2 years

Age of mother will be 30 more than the age of daughter

x+2=y+2+30

x=y+30     (2)

From (1) and (2), we get,

y+30=3y-20

30+20=3y-y

50=2y

y=25

Substituting y=25 in equation (1) we get,

x=3(25)-20

x=55

The present age of mother is 55 years and that of daughter is 25 years.