A shopkeeper gives books on rent for reading. She takes a fixed charge for the first two days, and an additional charge for each day thereafter. Latika paid Rs. 22 for a book kept for 6 days, while Anand paid Rs. 16 for the book kept for four days. Find the fixed charges and charge for each extra day.

Given:

A shopkeeper gives books on rent for reading. She takes a fixed charge for the first two days, and an additional charge for each day thereafter. Latika paid Rs. 22 for a book kept for 6 days, while Anand paid Rs. 16 for the book kept for four days.

To do:

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

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

Latika paid Rs. 22 for a book kept for 6 days.

This implies,

$x + 4y = 22$.....(i)

Anand paid Rs. 16 for a book kept for 4 days.

This implies,

$x + 2y = 16$.....(ii)

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

$(x+4y)-(x+2y)=22-16$

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

$2y=6$

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

$y=3$

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

$x+2(3)=16$

$x+6=16$

$x=16-6$

$x=10$

The fixed charge is Rs. 10 and the charge for each extra day is Rs. 3.   

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Updated on: 10-Oct-2022

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