A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs. 27 for a book kept for seven days, while Susy paid Rs. 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.

Given:

A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs. 27 for a book kept for seven days, while Susy paid Rs. 21 for the book she kept for five days. 

To do:

We have to find the fixed charge and the charge for each extra day.

Let the fixed charge for the first three days and the additional charge for each day thereafter be $x$ and $y$ respectively.

According to the question,

$x + 4y = 27$.....(i)

$x + 2y = 21$.....(ii)

Subtracting equation (ii) from equation (i), we get,

$(x+4y)-(x+2y)=27-21$

$x-x+4y-2y=6$

$2y=6$

$y=\frac{6}{2}$

$y=3$

Substituting $y=3$ in equation (ii), we get,

$x+2(3)=21$

$x+6=21$

$x=21-6$

$x=15$

The fixed charge is Rs. 15 and the charge for each extra day is Rs. 3.  

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Updated on: 10-Oct-2022

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