Question

Ravish tells his daughter Aarushi, "Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be. If present ages of Aarushi and Ravish are x and y years respectively, represent this situation algebraically and find their present ages.

• A. $x=12,y=49$
• B. $x=12,y=42$
• C. $x=10,y=49$
• D. $x=10,y=42$

Answer 1

Answer: (B)

$x=12,y=42$

Present Age of Ravish $=y$ years

Present Age of Aarushi $=x$ years

According to Question

$7$ Years ago,

$y-7=7(x-7)\Rightarrow 7x-y-42=\mathrm{0.............}\left(1\right)$

and $3$ Years from now

$y+3=3(x+3)\Rightarrow 3x-y+6=\mathrm{0............}\left(2\right)$

From (1) and (2)

$\left(1\right)-\left(2\right)\Rightarrow 7x-3x-y+y-42-6=0\Rightarrow 4x=48\Rightarrow x=12$

putting $x=12$ in Equation (2)

we get,

$3\times 12-y+6=0\Rightarrow y=42$