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
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!