Question

5 A lending library has a fixed charge for the first 3 days and an additional charge for each day thereafter. Ram returned a book after 1 week and paid Rs. 40 while Komal paid Rs. 60 as he returned it after 11 days. Find the fixed charge and the additional charge for each extra day paid by them. (use cross multiplication method)

Answer 1

$\large\underline{\sf{Solution-}}$

Let assume that

➢ Fixed charge for first 3 days be Rs x

and

➢ Per day additional charge after 3 days be Rs y.

According to first condition

➢ Ram returned a book after 1 week and paid Rs. 40.

It means,

➢ Ram used book 4 days extra.

➢ So, Ram have to pay Rs x for first 3 days and Rs 4y for additional 4 days thereafter.

$\rm :\longmapsto\:x + 4y = 40 - - - (1)$

According to second condition

➢ Komal paid Rs. 60 as he returned it after 11 days.

It means

➢ Komal used book 8 days extra.

➢ So, Komal have to pay Rs x for first 3 days and 8y for additional 8 days thereafter.

$\rm :\longmapsto\:x + 8y = 60 - - - (2)$

Now, we have two linear equations,

$\rm :\longmapsto\:x + 8y = 60$

and

$\rm :\longmapsto\:x + 4y = 40$

So, using Cross multiplication method, we have

$\begin{gathered}\boxed{\begin{array}{c|c|c|c} \bf 2 & \bf 3 & \bf 1& \bf 2\\ \frac{\qquad}{} & \frac{\qquad}{}\frac{\qquad}{} &\frac{\qquad}{} & \frac{\qquad}{} &\\ \sf 8 & \sf 60 & \sf 1 & \sf 8\\ \\ \sf 4 & \sf 40 & \sf 1 & \sf 4\\ \end{array}} \\ \end{gathered}$

$\rm :\longmapsto\:\dfrac{x}{320 - 240} = \dfrac{y}{60 - 40} = \dfrac{ - 1}{4 - 8}$

$\rm :\longmapsto\:\dfrac{x}{80} = \dfrac{y}{20} = \dfrac{ - 1}{ - 4}$

$\rm :\longmapsto\:\dfrac{x}{80} = \dfrac{y}{20} = \dfrac{1}{4}$

On multiply each term by 4, we get

$\rm :\longmapsto\:\dfrac{x}{20} = \dfrac{y}{5} = 1$

$\bf\implies \:\boxed{ \bf{ \: x = 20}} \: \: and \: \: \boxed{ \bf{ \: y = 5}}$

So,

Fixed charges for 3 days = Rs 20

Per day additional charge thereafter = Rs 5