Answer:
present age of man = 45 years
present age of daughter = 13 years
Explanation:
let present age of man = x, and
present age of daughter = y
according to the question:
5 years ago man's age was 5 times the age of his daughter,
x - 5 = 5(y - 5)
x - 5 = 5y - 25
x = 5y - 25 + 5
x = 5y - 20 (1)
in 3 years time twice of man's age will be equal to 6 times his daughter's age,
2(x + 3) = 6(y + 3)
2x + 6 = 6y + 18
2x = 6y + 18 - 6
2x = 6y + 12
x = 6y + 12 / 2 (2)
by comparing both equations (1) and (2)
5y - 20 = 6y + 12 / 2
10y - 40 = 6y + 12
10y - 6y = 12 + 40
4y = 52
y = 52/4 = 13
by substituting the value of y in equation (1)
x = 5(13) - 20
= 65 - 20
= 45
thus the present ages are,
man, x = 45 years
daughter, y = 13 years