Question

The difference of ages father and son is 30 years. After 7 years the sum of father and son is 66 years.so what is age of father?

Answer 1

• Let present age of father be "M" years and present age of son be "N" years.

》 The difference of ages father and son is 30 years.

According to question,

=> M - N = 30

=> M = 30 + N ________ (eq 1)

》 After 7 years the sum of father and son is 66 years.

Now..

• Age of father = (M + 7) years

• Age of son = (N + 7) years

According to question,

=> M + 7 + N + 7 = 66

=> M + N + 14 = 66

=> M + N = 52

=> 30 + N + N = 52 [From (eq 1)]

=> 30 + 2N = 52

=> 2N = 22

=> N = 11 (age of son)

Put value of N in (eq 1)

=> M = 30 + 11

=> M = 41 (age of father)

_____________________________

Age of father = 41 years.

___________ [ ANSWER ]

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☆ VERIFICATION :

From above calculations we have M = 41 and N = 11

Put value of M and N in this : M - N = 30

=> 41 - 11 = 30

=> 30 = 30

______________________________

Answer 2

$\bf{\huge{\underline{\boxed{\rm{\red{Answer:}}}}}}$

Given:-

• the difference of ages father and son is 30 years
• after 7 years the sum of father and son is 66 years

To find :-

• Age of father.

Solution :-

As per the first condition,

• the difference of ages father and son is 30 years.

Let the age of father be x years.

Let the age of son be y years.

We get our first equation from the first condition,

x - y = 30 ----> 1

As per the second condition,

• after 7 years the sum of father and son is 66 years.

Father's age = x + 7 years

Son's age = y + 7 years

Sum = 66 years

We will form our second equation,

x + 7 + y + 7 = 66

x + y + 7 + 7 = 66

x + y + 14 = 66

x + y = 66 - 14

x + y = 52 ----> 2

Add equation 1 to 2 and solve them simultaneously,

x - y = 30

x + y = 52

--------------

2x = 82

x = $\bf\large\frac{82}{2}$

x = 41

Substitute. this value of x in equation 1,

x - y = 30 ---->1

41 - y = 30

41 - 30 = y

11 = y

y = 11

Age of father = x = 41 years.

Age of son = y = 11 years.

$\bf{\large{\underline{\boxed{\tt{\purple{Verification:}}}}}}$

For first case :-

• The difference of ages father and son is 30 years.

Age of father = 41 years

Age of son = 11 years.

Difference = Age of father - Age of son

Difference = x - y

Difference given in question = 30

x - y = 30

41 - 11 = 30

30 = 30

LHS = RHS

For second case :-

• after 7 years the sum of father and son is 66 years,

After 7 years :-

Age of father = 41 + 7 = 48 years

Age of son = 11 + 7 = 18 years

Sum = Age of father + Age of son

Sum = x + y

Sum = 66 years

x + y = 66

48 + 18 = 66

66 = 66

LHS = RHS

Hence the equations are verified.