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Pair of Linear Equations in Two Variables — Maths STD 10 — Question

Gujarat BoardEnglish MediumSTD 10MathsPair of Linear Equations in Two Variables2 Marks
Question
A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid $₹ 27$ for a book kept for seven days, while Susy paid $₹ 21$ for the book she kept for five days. Find the fixed charge and the charge for each extra day. Solve the pair of the linear equation obtained by the elimination method.
✓

Answer

Suppose the fixed charge be Rs. x and the extra charge per day be Rs y.
According to the question, Mona paid Rs 27 for a book kept for 7 days,
$\Rightarrow$ $x + 4y = 27$$........(i)$
Tanvy paid $Rs.21$ for a book kept for 5 days,
$\Rightarrow$ $x+ 2y = 21$$.........(ii)$
Subtracting $(ii)$ from $(i)$,
$\Rightarrow 2y = 6$
$\Rightarrow$ $y = 3$
Substituting $y = 3$ in $(ii),$ we get $x = 15$
The fixed charge is $Rs.\ 15$ and the charge per day is $Rs\ 3$.

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