Question

1) If we interchanged digits in the age of father. We get age of his son the number
in age of father and son is a natural number. If the sum of the ages of father and son
is 55 years. Find their present age
Tabda​

Answer 1

Hi there!

Here's the answer:

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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

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

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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

•°• Given Data Matched.

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:)

Hope it helps!

Answer 2

the present age of father is 41 years
the present age of son is 14 years