Question

Form the pair of linear equations for the following problems and find their solution by 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?

Answer 1

Let the present age of \(\mathrm{Nurl}=\mathrm{x} \mathrm{yr}\)
And the present age of sonu \(=y\) yr
Five years ago,
Nuri's age \(=(x-5) y r\)
Sonu's age \(=(y-5) y r\)
According to the question,
$$
\begin{aligned}
&(x-5)=3(y-5) \\
&=x-5=3 y-15 \\
&=x-3 y=-10 \ldots \text { (i) }
\end{aligned}
$$
After ten years,
$$
\begin{aligned}
&\text { Aftab's age }=(x+10) \text { yr } \\
&\text { Daughter's age }=(y+10) y r
\end{aligned}
$$
According to the question,
$$
\begin{aligned}
&(x+10)=2(y+10) \\
&=x+10=2 y+20 \\
&=x-2 y=10 \ldots(\text { ii })
\end{aligned}
$$
Now, we can solve this by an elimination method
On subtracting Eq. (II) from (I) we get
$$
\begin{aligned}
&x-2 y-x+3 y=10-(-10) \\
&=-2 y-3 y=10+10 \\
&=y=20
\end{aligned}
$$
On putting \(y=20\) in Eq. (I) we get
$$
\begin{aligned}
&x-3(20)=-10 \\
&=x-60=-10 \\
&=x=50
\end{aligned}
$$
Hence, the age of Nurl Is 50 years and age of sonu is 20 years.

Answer 2

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Answer 3

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