Question

D) Five years ago, a woman was four times as old as her daughter. In four years time, the woman will be two and half times as old as her daughter. Find their present ages?

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Answer 1

Let's say the woman's age is currently x and the daughter's age is y.

Five years ago, the woman was x-5 years old and the daughter was y-5 years old. So, the relationship between their ages five years ago can be expressed as:

(x-5) = 4(y-5)

Solving this equation for x, we get:

x = 4y - 15

In four years time, the woman will be x+4 years old and the daughter will be y+4 years old. The relationship between their ages in four years time can be expressed as:

(x+4) = 2.5(y+4)

Substituting the expression for x that we derived earlier into this equation, we get:

(4y-15+4) = 2.5(y+4)

This simplifies to:

4y-11 = 2.5y+10

Solving this equation for y, we get:

y = 11

Substituting this value back into the expression for x, we get:

x = 4(11) - 15 = 43

So, the woman is currently 43 years old and the daughter is currently 11 years old.

Explanation: