Question

Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method:

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

• A. Fixed charge $=Rs.3$ , Per day extra charge $=Rs.5$
• B. Fixed charge $=Rs.5$ , Per day extra charge $=Rs.3$
• C. Fixed charge $=Rs.4$ , Per day extra charge $=Rs.5$
• D. Fixed charge $=Rs.5$ , Per day extra charge $=Rs.4$

Answer 1

The correct option is B Fixed charge $=Rs.5$ , Per day extra charge $=Rs.3$

let the fixed charges=x and additional charges=y
According to the question
$\Rightarrow 3x+4y=\mathrm{27....}eq1$
$\Rightarrow 3x+2y=\mathrm{21....}eq2$
$subtracteq1andeq2$
$\Rightarrow (3x+4y=27)-(3x+2y=21)\Rightarrow 2y=6\Rightarrow y=3$
$putx=3ineq1$
$\Rightarrow 3x+4\times 3=27\Rightarrow 3x=15\Rightarrow x=5$
Fixed charges=5 Rs.
The charge for each extra day=3 Rs.