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

Solution :-

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 :-

$\longrightarrow \sf x - y = 10 \\\\\longrightarrow x = y+10 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .................(1)$

According to the second condition :-

$\longrightarrow \sf x+5=2(y+5) \\\\\longrightarrow x+5 = 2y+110 \\\\\longrightarrow x-2y = 10-5 \\\\\longrightarrow x-2y = 5 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .................(2)$

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

$\longrightarrow \sf y+10-2y = 5 \\\\\longrightarrow y-2y = 5-10 \\\\\longrightarrow -y = -5 \\\\\longrightarrow \bf y = 5$

Substitute y = 5 in eq(1) :-

$\longrightarrow \sf x=5+10 \\\\\longrightarrow \bf x = 15$

Present age of Ram = 15 years

Present age of Gaurav = 5 years

Answer 2

Step-by-step explanation:

Let

• present age of Ram= x
• present age of Gaurav=y

ATQ

$\\\qquad\quad\displaystyle\sf {:}\longrightarrow x-y=10$

$\\\qquad\quad\displaystyle\tt {:}\longrightarrow x=y+10\dots\dots (1)$

After 5years

• Age of Ram=x+5
• Age of Gaurav=y+5

Again,

$\\\qquad\quad\displaystyle\sf {:}\longrightarrow x+5=2 (y+5)$

$\\\qquad\quad\displaystyle\sf {:}\longrightarrow x+5=2y+10$

$\\\qquad\quad\displaystyle\sf {:}\longrightarrow x-2y+5-10=0$

$\\\qquad\quad\displaystyle\sf {:}\longrightarrow x-2y-5=0$

$\\\qquad\quad\displaystyle\tt {:}\longrightarrow x-2y=5\dots\dots (2)$

From eq (1) substitute the value of x in eq (2)

$\\\qquad\quad\displaystyle\sf {:}\longrightarrow y+10-2y=5$

$\\\qquad\quad\displaystyle\sf {:}\longrightarrow y-2y+10=5$

$\\\qquad\quad\displaystyle\sf {:}\longrightarrow -y+10-5=0$

$\\\qquad\quad\displaystyle\sf {:}\longrightarrow -y+5=0$

$\\\qquad\quad\displaystyle\sf {:}\longrightarrow -y=-5$

$\\\qquad\quad\displaystyle\bf {:}\longrightarrow y=5$

• Substitute the value of y in eq (1)

$\\\qquad\quad\displaystyle\sf {:}\longrightarrow x=5+10$

$\\\qquad\quad\displaystyle\bf {:}\longrightarrow x=15$

$\\\\\therefore{\underline{\boxed{\bf (x,y)=(15,5)}}}$