Question

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 $₹22$for a book kept for six days, while Anand paid $₹16$ for the book kept for four days.

Find the fixed charges and the charge for each extra day.

• A. $₹13,₹2$
• B. $₹10,₹3$
• C. $₹12,₹9$
• D. $₹14,₹5$

Answer 1

The correct option is B

$₹10,₹3$

Let the fixed charge for two days be $₹$$\mathrm{x}$ and the additional charge be $₹\mathrm{y}$ per day

Step 1: Form the linear equation in two variables for Latika:

Number of days for Latika $=6=2+4$

$\therefore$ Charges for Latika$=\mathrm{Fixed}\mathrm{charge}\mathrm{for}\mathrm{two}\mathrm{days}+4\times \mathrm{Additional}\mathrm{charge}\mathrm{per}\mathrm{day}$

$=\mathrm{x}+4\mathrm{y}$

And, it is given that Latika paid $₹22$

$\begin{array}{rcl}\therefore \mathrm{x}+4\mathrm{y}& =& 22\\ \mathrm{x}& =& 22-4\mathrm{y}.......\left(1\right)\end{array}$

Step 2: Form the linear equation in two variables for Anand:

Number of days for Anand $=4=2+2$

$\therefore$ Charge for Anand$=\mathrm{Fixed}\mathrm{charge}\mathrm{for}\mathrm{two}\mathrm{days}+2\times \mathrm{Additional}\mathrm{charge}\mathrm{per}\mathrm{day}$

$=\mathrm{x}+2\mathrm{y}$

And, it is given that Anand paid$₹16$

$\begin{array}{rcl}\therefore \mathrm{x}+2\mathrm{y}& =& 16\\ \mathrm{x}& =& 16-2\mathrm{y}.........\left(2\right)\end{array}$

Step 3: Solve for $\mathrm{x}$ and $\mathrm{y}$:

On comparing equation ($1$) and ($2$), we get,

$\begin{array}{rcl}& \Rightarrow & 22-4\mathrm{y}=16-2\mathrm{y}\\ 2\mathrm{y}& =& 6\\ \mathrm{y}& =& ₹3\end{array}$

Substituting $\mathrm{y}=3$ in equation ($1$), we get,

$\begin{array}{rcl}& \Rightarrow & \mathrm{x}=22-4\left(3\right)\\ & =& 22-12\\ & =& ₹10\end{array}$

Therefore, a fixed charge for two days$=₹10$ and an additional charge$=₹3$ per day

Hence, the correct option is ($\mathrm{B}$)