Question

The difference between present ages of Ram and Gaurav is 10 years. After 5 years, Ram's age will be twice of Gaurav's age. The present age (in years) of Ram is​

Answer 1

Answer:

Let :-

Present age of Ram = x

Present age of Gaurav = y

After 5 years :-

Age of Ram = x + 5

Age of Gaurav = y + 5

According to the first condition :-

\begin{gathered}\longrightarrow \sf x - y = 10 \\\\\longrightarrow x = y+10 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .................(1)\end{gathered}

⟶x−y=10

⟶x=y+10 .................(1)

According to the second condition :-

\begin{gathered}\longrightarrow \sf x+5=2(y+5) \\\\\longrightarrow x+5 = 2y+110 \\\\\longrightarrow x-2y = 10-5 \\\\\longrightarrow x-2y = 5 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .................(2)\end{gathered}

⟶x+5=2(y+5)

⟶x+5=2y+110

⟶x−2y=10−5

⟶x−2y=5 .................(2)

Substitute the value of x in eq(2) :-

\begin{gathered}\longrightarrow \sf y+10-2y = 5 \\\\\longrightarrow y-2y = 5-10 \\\\\longrightarrow -y = -5 \\\\\longrightarrow \bf y = 5\end{gathered}

⟶y+10−2y=5

⟶y−2y=5−10

⟶−y=−5

⟶y=5

Substitute y = 5 in eq(1) :-

\begin{gathered}\longrightarrow \sf x=5+10 \\\\\longrightarrow \bf x = 15\end{gathered}

⟶x=5+10

⟶x=15

Present age of Ram = 15 years

Present age of Gaurav = 5 years