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# 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

$₹13,₹2$

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B

$₹10,₹3$

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C

$₹12,₹9$

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D

$₹14,₹5$

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Solution

## The correct option is B $₹10,₹3$Let the fixed charge for two days be $₹$$\mathrm{x}$ and the additional charge be $₹\mathrm{y}$ per dayStep 1: Form the linear equation in two variables for Latika:Number of days for Latika $=6=2+4$$\therefore$ Charges for Latika$=\mathrm{Fixed}\mathrm{charge}\mathrm{for}\mathrm{two}\mathrm{days}+4×\mathrm{Additional}\mathrm{charge}\mathrm{per}\mathrm{day}$ $=\mathrm{x}+4\mathrm{y}$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$=\mathrm{Fixed}\mathrm{charge}\mathrm{for}\mathrm{two}\mathrm{days}+2×\mathrm{Additional}\mathrm{charge}\mathrm{per}\mathrm{day}$ $=\mathrm{x}+2\mathrm{y}$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,$\begin{array}{rcl}& ⇒& 22-4\mathrm{y}=16-2\mathrm{y}\\ 2\mathrm{y}& =& 6\\ \mathrm{y}& =& ₹3\end{array}$Substituting $\mathrm{y}=3$ in equation ($1$), we get, $\begin{array}{rcl}& ⇒& \mathrm{x}=22-4\left(3\right)\\ & =& 22-12\\ & =& ₹10\end{array}$Therefore, a fixed charge for two days$=₹10$ and an additional charge$=₹3$ per dayHence, the correct option is ($\mathrm{B}$)  Suggest Corrections  27      Similar questions  Explore more