Question

Seven years ago, a father was seven times as old as his son was. three years hence, he will be three times as old as his son. Find their present ages.

Answer 1

Answer:

present ags of :

father : x

son : y

seven years ago , the age of

father : x - 7

son : y - 7

by the given data

(x - 7) = 7(y -7)

x - 7 = 7y - 49

x = 7y - 49 + 7

x = 7y - 42. ..............(a)

after three years, their ages will be

father : x + 3

son : y + 3

by the given data

(x+3) = 3(y+3)

x + 3 = 3y + 9

x = 3y + 9 - 3

x = 3y + 6. .............(b)

joining (a) and (b)

7y - 42 = 3y + 6

7y - 3y = 6 + 42

4y = 48

y = 12. ..........(c)

substituting the value of y either in (a) or (b)

here I am substituting it in (b)

3y + 6 = x

(3 * 12) + 6 = x

36 + 6 = x

42 = x

therefore the value of x = 42 and y = 12