Question

A local bus is carrying 40 passengers, some with Rs.5 tickets and the remaining with Rs.7.50 tickets. If the total receipts from these passengers are Rs.230, find the number of passengers with Rs.5.

Answer 1

Hint: These type of questions can be solved by considering the unknown value here it will be number of passengers with Rs.5 ticket as a variable \[\left( x \right)\] and from the given data in the question number of passengers with Rs.7.50 ticket will be equal \[40 - x\], we should form a relative equation using the data and solve the equation to get the required unknown value.

Complete step-by-step solution:
Given that a local bus is carrying 40 passengers, some passengers pay Rs.5 for the ticket and the remaining pay Rs.7.50 for the ticket, and also given that the total receipts count to Rs.230 of all these passengers.
Now from the data given,
Total number of passengers in the bus= 40.
Total amount count = Rs.230,
Now consider that the number of passengers with Rs.5 ticket =\[x\],
Then number of passengers with Rs.7.50 ticket will be =\[40 - x\],
According to the given question,
Total amount of passengers with Rs.5 =\[5 \times x\],
Amount of passengers with Rs.7.50 =\[\left( {40 - x} \right) \times 7.50\],
From the given data,
Total amount of passengers with Rs.5 + Total amount of passengers with Rs.5=Total amount
By substituting the values we get the equation,
$\Rightarrow$\[5x + \left( {40 - x} \right) \times 7.50 = 230\],
Now simplifying by doing multiplication we get,
$\Rightarrow$\[5x + 300 - 7.50x = 230\],
Now taking all \[x\] terms to one side we get,
$\Rightarrow$\[5x - 7.50x = 230 - 300\],
Now further simplifying we get,
$\Rightarrow$\[ - 2.5x = - 70\],
Now dividing both sides with -2.5 we get,
$\Rightarrow$\[\dfrac{{ - 2.5x}}{{ - 2.5}} = \dfrac{{ - 70}}{{ - 2.5}}\],
Now eliminating like terms, and taking out decimals we get,
$\Rightarrow$\[x = \dfrac{{70 \times 10}}{{25}}\],
Further simplifying we get,
$\Rightarrow$\[x = 28\].
The number of passengers with Rs.5 ticket = 28.

\[\therefore \]The number of passengers in the bus with a Rs.5 ticket will be 28, and the number of passengers with a Rs.7.50 ticket will be 12.

Note: A linear equation in one variable is an equation in which only one unknown quantity is present in the equation. Here are the steps to solve linear equation in one variable,
First observe the linear equations.
Next, find out what quantity we have to find.
Now part the equation in two parts as L.H.S and R.H.S.
Transfer all the constants on the Right Hand Side (R.H.S) of the equation and variables on the Left Hand Side (L.H.S.) of the equation.
Perform the algebraic operations on both sides of the equation to get the value of the variable.