Question

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. [4 MARKS]

Answer 1

Concept : 1 Mark
Application : 1 Mark
Calculation : 2 Marks

Let the fixed charge for 3 days be $x$

And charge per extra day be $y$

Saritha kept books for seven days

$\therefore$ Saritha has 4 extra days.

Susy kept books for five days

$\therefore$ Susy has 2 extra days.

According to given condition,

$x+4y=27\dots \dots \left(i\right)$

$x+2y=21\dots \dots \left(ii\right)$

Solving (i) and (ii) ,

$x=27-4y$ [From (i)]

Substituting value of x in (ii)

$x+2y=21$

$27-4y+2y=21$

$27-2y=21\Rightarrow y=3$

Now, $x=27-4y$

$x=27-4\left(3\right)\Rightarrow x=15$

$y=3,x=15$