Question

A passenger is allowed some free luggage by Rajdhani express. Two passengers have a total of $105kg$ luggage and they have to pay $Rs.18$ and $Rs.12$ as luggage charges respectively. If one passenger having the same $kg$ of luggage then he would have to pay $Rs.36$, find how much free luggage each passenger is allowed to carry.

Answer 1

Let the free luggage allowed be $xkg$ and the charge paid for each $kg$ more than $x=Rs.y$

Then according to the question,

105kgTwo passengers have a total of $105kg$ luggage and they have to pay $Rs.18$Rs.18 and $Rs.12$ with some $xkg$ as free luggage .Rs.12

$\therefore y(105-(x+x\left)\right)=12+18$

$105-2x=\frac{30}{y}-----\left(i\right)$

Also, If one passenger having the same $kg$ of luggage then he would have to pay $Rs.36$, therefore,

$y(105-x)=36$

$105-x=\frac{36}{y}-----\left(ii\right)$

Multiplying $\left(i\right)$ by $36$ and $\left(ii\right)$ by $30$ we get,

$\frac{\begin{array}{c}3780-72x=\frac{1080}{y}\\ 3150-30x=\frac{1080}{y}\\ -+-\end{array}}{630-42x=042x=630}$

$x=\frac{630}{42}=15$

$\therefore$ Free luggage allowed $=15kg$

From $\left(i\right)$ we get,

$105-2\left(15\right)=\frac{30}{y}$

$105-30=\frac{30}{y}$

$y=\frac{30}{75}=0.4$

$y=Rs.0.40=40$ paise

Let us check $\left(ii\right)$

$y(105-x)=30$

$0.4(105-15)=0.4\left(90\right)$

$=36$