Question

8. A father is 5 times as old as his son. In 18 years, the father will be twice
as old as his son. How old is the father at present?
A.
B.
C.
D.
20 years
30 years
50 years
40 years

Answer 1

Answer:

option C 30 years

Step-by-step explanation:

Let the age of Father = x

let the age of son = y

x = 5y

After 18 years

x+18 = 2(y+18)

5y+18 = 2y+36

5y-2y = 36-18

3y = 18

y = 6

x = 5(6)

x = 30

Answer 2

The father is 30 years old at present

Given :

• A father is 5 times as old as his son.

• In 18 years, the father will be twice as old as his son

To find :

The present age of the father is

A. 20 years

B. 30 years

C. 50 years

D. 40 years

Solution :

Step 1 of 2 :

Form the equation to calculate present age of the father

Let present age of the son = x years

Since father is 5 times as old as his son

So present age of the father = 5x years

Now in 18 years, the father will be (5x + 18) years old and his son will be (x + 18) years old

By the given condition

$\displaystyle \sf (5x + 18) = 2(x + 18)$

Step 2 of 2 :

Calculate present age of the father

$\displaystyle \sf (5x + 18) = 2(x + 18)$

$\displaystyle \sf{ \implies }5x + 18 = 2x + 36$

$\displaystyle \sf{ \implies }5x - 2x = 36 - 18$

$\displaystyle \sf{ \implies }3x = 18$

$\displaystyle \sf{ \implies }x = 6$

∴ Present age of the father

= 5x years

= (5 × 6) years

= 30 years

Hence the correct option is B. 30 years

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