Question

The difference between the ages of Gopal and his father is 26 years if the sum of their ages is 56 years find the ages of Gopal and his father

Answer 1

Step-by-step explanation:

Answer:

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

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

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

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

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

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

$\rule{180}{1.5}$

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

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

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

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