Question

Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method:

Five years ago Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?

• A. Nuri is $40$ years old and Sonu is$10$years old.
• B. Nuri is $50$ years old and Sonu is$20$ years old.
• C. Nuri is $70$ years old and Sonu is $30$ years old.
• D. Nuri is $60$ years old and Sonu is $10$ years old.

Answer 1

Answer: (B)

Nuri is $50$ years old and Sonu is$20$ years old.

Let present age of Nuri= $x$ years
Let present age of sonu=$y$ years
Five years ago
Nuri was $(x-5)years$
Sonu was $(y-5)years$
According to the first condition
$\Rightarrow (x-5)=3(y-5)$
$\Rightarrow x-5=3y-15\Rightarrow x-3y=-\mathrm{10.........}eq1$
Ten years later
Nuri will be $(x+10)years$
Sonu will be $(y+10)$
$\Rightarrow (x+10)=2(y+10)$
$\Rightarrow x+10=2y+20\Rightarrow x+2y=\mathrm{10.....}eq2$
Subtracting $eq1andeq2$
$\Rightarrow -y=-2-\Rightarrow y=20$
put y=20 in $eq1$
$x-3y=10\Rightarrow x=10-60\Rightarrow x=50$
Hence, present age of Nuri= 50 years
Let present age of sonu=20 years