Question

sum of age of Samuel and his father is 47. When Samuel reaches his father's age, sum of their age will be 97. How old is Samuel right now?

Answer 1

S = present Samuel’s age

F = present father’s age

Sum of age of Samuel and his father is 47.

S + F = 47

S = 47 - F

After x yrs Samuel will be S + x yrs old

Father wil be F + x yrs old.

After x yrs sum of Samuel’s age and father’s age will be 97.

S + x + F + x = 97

S + F + 2 x = 97

Replace S + F = 47 in this equation

47 + 2 x = 97

2 x = 97 - 47

2 x = 50

x = 50 / 2 = 25

After 25 yrs Samuel’s age will be equal present father’s age.

When Samuel reaches his father's age Samuel’s age will be equal present father’s age.

In this time S = F

Father’s age will be F + x = F + 25

Sum of their age will be 97.

F + F + 25 = 97

2 F = 97 - 25

2 F = 72

F = 72 / 2 = 36

Present father’s age = 36

Put this value in equation:

S = 47 - F

S = 47 - 36 = 11

Present Samuel’s age = 11


Proof:

Sum of their preset age = 36 + 11 = 47

After 25 yrs Samuel will be 11 + 25 = 36 yrs old, Father wil bee 36 + 25 = 61 yrs old.

36 + 61 = 97

Answer 2

Samuel is X years old.
His father is Y years old.

Eq1: x + y = 47.

y + (y+25) = 97,
Y = 36.

In Eq1, replace Y with 36 and solve for X:
x + 36 = 47,
X = 11.