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P-1 Linear Equations in Two Variables — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsP-1 Linear Equations in Two Variables3 Marks
Question
A certain amount is equally distributed among certain number of students. Each would get ₹ 2 less if 10 students were more and each would get ₹ 6 more if 15 students were less. Find the number of students and the amount distributed.
✓

Answer

Let the number of students be $x$ and amount given to each stud be ₹ $y$.
$\therefore$ Total amount distributed is $x y$
From the first condition we get,
$\begin{aligned}
& (x+10)(y-2)=x y \\
& \therefore x y-2 x+10 y-20=x y \\
& \therefore-2 x+10 y=20 \\
& \therefore-x+5 y=10 \ldots \text { (I) }
\end{aligned}$
From the $2^{\text {nd }}$ condition we get,
$\begin{aligned}
& (x-15)(y+6)=x y \\
& \therefore x y+6 x-15 y-90=x y \\
& \therefore 6 x-15 y=90 \\
& \therefore 2 x-5 y=30 \ldots \text { (II) }
\end{aligned}$
Adding equations (I) and (II)
$\begin{aligned}
-x+5 y & =10 \\
^+ 2 x-5 y & =30 \\
\hline x & =40
\end{aligned}$
Substitute this value of $x$ in equation (I)
$\begin{gathered}
-x+5 y=10 \\
\therefore-40+5 y=10 \\
\therefore \quad 5 y=50 \\
\therefore \quad y=10
\end{gathered}$
Total amount distributed is $=x y=40 \times 10=₹ 400$.
$\therefore \quad ₹ 400$ distributed equally among 40 students.

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