Question

the difference between the ages of gopal land his father is 26 years.if the sum of their ages is 56 years.find the age of gopal and his father

Answer 1

GIVEN :-

• difference between the ages of gopal and his father is 26 years.
• sum of their ages is 56 years.

TO FIND :-

• The age of gopal and his father.

SOLUTION :-

Let the age of gopal be "y" years and age of father be "x" years.

➠ Father age - Gopal age = 26

➠ x - y = 26

➠ x = 26 + y .....Eq(1)

Similarly,

➠ Gopal age + Father age = 56

➠ x + y = 56

Now substitute the value of x from Equation 1.

➠ 26 + y + y = 56

➠ 26 + 2y = 56

➠ 2y = 56 - 26

➠ y = 30/2

➠ y = 15

Now put the value of y in Equation 1.

➠ x = 26 + y

➠ x = 26 + 15

➠ x = 41

Hence the age of son is 15 years and age of father is 41 years.

Answer 2

Answer:

Let the Age of Gopal be x and Age of his Father be y.

$\underline{\bigstar\:\textsf{According to the given Question :}}$

$\underline{\bf Statement\:\textit{1 :}}$

$:\implies\sf Father-Gopal=26\\\\\\:\implies\sf y-x=26\qquad eq. - 1$

$\underline{\bf Statement\:\textit{2 :}}$

$:\implies\sf Father+Gopal=56\\\\\\:\implies\sf y+x=56\qquad eq. - 2$

$\rule{180}{1.5}$

$\underline{\bigstar\:\textsf{Adding eq. 1 and eq. 2 :}}$

$:\implies\sf y - x = 26\\\\:\implies\sf y + x = 56 \\ \frac{ \qquad \qquad \qquad \qquad \qquad \quad}{} \\:\implies\sf (y + y) = 26 + 56\\\\\\:\implies\sf 2y = 82\\\\\\:\implies\sf y = \dfrac{82}{2}\\\\\\:\implies\sf y = 41 \:years \qquad\bf\bigg\lgroup Father's\: Age\bigg\rgroup$

$\underline{\bigstar\:\textsf{Putting value of y in eq. 2 :}}$

$:\implies\sf y+x=56\\\\\\:\implies\sf 41+x=56\\\\\\:\implies\sf x=56-41\\\\\\:\implies\sf x=15\:years\qquad\bf\bigg\lgroup Gopal's\: Age\bigg\rgroup$