A lending library has a fixed charge for the first three days and… - Vidyadip

Question

A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Mona paid $₹ 27$ for a book kept for $7$ days, while Tanvy paid $₹ 21$ for the book she kept for $5$ days. Find the fixed charge and the charge for each extra day.

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Answer

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

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