Question

When you reverse the digits of age of father, you will get the age of son. One year ago the age of father was twice that of sons age. What are the current ages of father and son?

Answer 1

Answer:

Let present age of father = 10x+y

where y- units digit of his age

& x - tens digit of his age

Reversing digits gives son's present age

=> Son's present age = 10y+x

Given that,

One year Ago,

Father's age = (10x+y) - 1

Son's age = (10y+x) - 1

Father's Age = 2 × (Son's age)

=> (10x+y) - 1 = 2 × [ (10y+x) - 1 ]

=> 10x+y-1 = 20y+2x-2

=> 8x-19y = -1

=> 8x = 19y-1

=> x = (19/8)y - (1/8)

To make satisfy the above condition satisfied, replace the values of x & y

• When y = 0

x - doesn't satisfy the condition

• When y = 1

x - doesn't satisfy the condition

• When y = 2

x - doesn't satisfy the condition

The only set of digits that satisfies this is

y = 3 & x = 7.

Father's present age = 10x+y = 73

and Son's present age = 10y+x = 37

Verification:

F - Father's Age ; S - Son's age

F = 73

S = 37

One year ago,

F = 72

S = 36 = (1/2) × F = (1/2) × 72

Step-by-step explanation: