Question

Q.5) Magesh was 6 times older than his
daughter 12 years ago. He would be 2 time
older than her age 20 years from now. Fou
years hence, what was the ratio of his age to
that of his daughter?
a) 2:5
b) 1:4
c) 8:3
d) 4: 5
e) 2:3​

Answer 1

Answer:

c) 8:3

Step-by-step explanation:

Let the present age of the daughter = x

Let the present age of the father = y

Their ages 12 years ago:

Age of the daughter 12 years ago = x - 12

Age of the father 12 years ago = y - 12

Given;

Age of the father was 6 times the age of daughter

y - 12 = 6(x - 12)

y - 12 = 6x - 72

6x - y - 60 = 0     ——- Eq(1)

Their ages after 20 years:

Age of the daughter 20 years from now = x + 20

Age of the father 20 years from now = y + 20

Given;

Age of the father will be 2 times the age of daughter

y + 20 = 2(x + 20)

y + 20 = 2x + 40

2x - y + 20 = 0      ——- Eq(2)

Solving Eq(1) & Eq(2);

    2x - y + 20 = 0

   6x - y - 60 = 0   (-)   (+) (+)

   ———————

   -4x + 80 = 0

    4x = 80

      x = 20

From Eq(2);

2x - y + 20 = 0

2(20) - y + 20 = 0

40 - y + 20 = 0

y = 60

Ratio of the father’s age to his daughter 4 years hence

= 60 + 4 : 20 + 4

= 64 : 24

= 8:3