Question

A lending library has a fixed charge for the first three days and an additional charge for everyday thereafter. Saritha paid Rs $27$ for a book kept for $7$ days while Susy paid Rs $21$ for a book she kept for $5$ days. Find the fixed charge and the charge for each extra day.
(a) Fixed charge is Rs $12$ charge for extra day: Rs $9$
(b) Fixed charge Rs \[x\], charge for each extra day: Rs $3$
(c) Fixed charge Rs $18$, charge for each extra day: Rs $3$
(d) Data insufficient

Answer 1

Hint:In this question we will form a linear equation using given data and solve it using substitution method.As there are two variables say x for fixed charge and y for variable there will be two equations.

Complete step-by-step answer:
Let us assume that the fixed charge for the first three days of a lending library to be Rs x. And let the charge for each additional day of lending library be Rs y.
We are given that Saritha has kept a book for seven days. So, for the first three days, she would have paid a fixed charge, that is Rs x and for each of the remaining days, that is $7-3=4$ days, she would have paid additional charges, that is Rs $4y$. Also, in total, she has paid Rs 27, that is the sum of fixed and additional changes.
Therefore, we get,
$x+4y=27......(i)$
Next, we are given that Susy has kept a book for 5 days. So, for the first three days, she would have paid fixed charges, that is Rs x and for each of the remaining days, that is $5-3=2$ days, she would have paid additional charges, that is Rs $2y$. Also, in total, she has paid Rs $21$, that is the sum of fixed and additional charges.
Therefore, we get,
$x+2y=21$
Here, subtraction $2y$ from both sides of the equation, we get,

$x=21-2y........(ii)$
Now, substituting this value of x in equation (i), we get.
$\left( 21-2y \right)+4y=27$
$\Rightarrow 21-2y+4y=27$
$\Rightarrow 21+2y=27$
Subtracting 21 from both the sides of the equation, we get.
$21+2y-21=27-21$
$\Rightarrow 2y=6$
Dividing 2 from both sides of the equation, we get,
\[\dfrac{2y}{2}=\dfrac{6}{2}\]
\[\Rightarrow y=3\]
Now putting \[y=3\] in equation (II), we get,
\[x+2\left( 3 \right)=21\]
\[\Rightarrow x+6=21\]
Subtracting 6 from both sides of the equation, we get,
\[x+6-6=21-6\]
\[\Rightarrow x=15\]
Hence, the fixed charge for the library is Rs \[15\] and an additional charge of each day is Rs \[3\].
Therefore (b) is the correct option.

Note: In this equation, the fixed price is for three days together, so do not confuse it to be for each of the first three days and take \[3x\] instead of \[x\].