Question

5 years ago a mother was 7 times as old as her daaughter 5 years hence . she will be 3 times as old as her daughter. find their present ages

Answer 1

Hi!

Here is the answer to your question.

Let the present ages of mother and daughter be M and D respectively.

According to the question,

5 years ago,

M – 5 = 7 (D – 5) … (1)

5 years hence,

M + 5 = 3 (D + 5) … (2)

Subtracting equation (1) from equation (2),

(M + 5) – (M – 5) = 3 (D + 5) – 7 (D – 5)

M + 5 – M + 5 = 3D + 15 – 7D + 35

10 = –4D + 50

4D = 50 – 10

4D = 40

D = 40 ÷ 4 = 10

By putting this value into equation (1),

M – 5 = 7 (10 – 5)

M – 5 = 7 × 5

M – 5 = 35

M = 35 + 5

M = 40

Present age of daughter = 10 years

Present age of mother = 40 years

Cheers!