Question

The sum of the ages of a father and his son is 70 . Five years ago difference between their age is 14 .The father's present age is​

Answer 1

here is your answer......

this way

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Answer 2

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Given :-

• The sum of the ages of a father and his son is 70
• Five years ago difference between their age is 14

To find :-

• Present age of Father

Solution :-

Let the present age of son be x years

Let the present age of father be y years.

As per first condition :-

• The sum of the ages of a father and his son is 70

Let's represent the given condition mathematically to obtain our first equation.

x + y = 70 -----> 1

As per second condition :-

• Five years ago difference between their age is 14

Ages 5 years ago :-

Son = x - 5 years

Father = y - 5 years.

Difference = 14

Let's represent this mathematically.

x - 5 - y - 5 = 14

x - y - 5 - 5 = 14

x - y - 10 = 14

x - y = 14 + 10

x - y = 24 ----> 2

Solve equations 1 and 2 simultaneously by elimination method.

Subtract equation 2 from 1,

.....+ x + y = + 70

- ( + x - y = + 24 )

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2x = 56

x = $\large\frac{56}{2}$

x = 28

Substitute x = 28 in equation 1,

x + y = 70 -----> 1

28 + y = 70

y = 70 - 28

y = 42

•°• Present age of Son = 28 years

Present age of Father = 42 years

$\bf{\huge{\underline{\boxed{\tt{\red{Verification:}}}}}}$

For first case :-

• The sum of the ages of a father and his son is 70

Present age of Son = 28 years = x

Present age of Father = 42 years = y

Sum of ages = 70

x + y = 70

28 + 42 = 70

70 = 70

LHS = RHS.

For second case :-

• Five years ago difference between their age is 14

Ages five years ago :-

Son = x - 5 = 28 - 5 = 23 years

Father = y - 5 = 42 - 5 = 37 years

Difference = 14

y - x = 14

37 - 23 = 14

14 = 14

LHS = RHS

Hence verified.