Question

The ratio of first and second class train fares between two stations is 3:1 and that of the number of passengers travelling between these stations by first and second class is 1:50. If on a particular day Rs.1325 be collected from the passengers travelling between these stations, then the amount collected from the second class passengers is:
(a) Rs.1250
(b) Rs.1000
(c) Rs.850
(d) Rs.750

Answer 1

Hint: We will first assume the fares of first class as 3x and that of second class as x. Then we will calculate the total fare collected in both the classes by summing up the number of people in those classes multiplied by the fare per person. And finally we will equate it to Rs. 1325.

Complete step-by-step answer:
Let the fares for 1st class passengers be 3x and the fare for 2nd class passengers be x.
And the number of passengers travelling between two stations is 1 for 1st class and 50 for 2nd class.
Now the total fare of first class collected is the number of passengers in 1st class multiplied by the fare of first class. Using this information we get,
Fare collected from first class \[=3x\times 1=3x..........(1)\]
Again, the total fare of the second class collected is the number of passengers in 2nd class multiplied by the fare of second class. Using this information we get,
Fare collected from second class \[=x\times 50=50x..........(2)\]
Now adding equation (1) and equation (2) and then equating it with the total fare collected in one day. So using this information we get,
\[\Rightarrow 3x+50x=1325..........(3)\]
Now adding the like terms and solving for x in equation (3) we get,
\[\begin{align}
  & \Rightarrow 53x=1325 \\
 & \Rightarrow x=\dfrac{1325}{53}=25.......(4) \\
\end{align}\]
Hence substituting the value of x from equation (4) in equation (2) we get,
Fare collected from second class \[=25\times 50=1250\]
Hence the right answer is option (a).

Note: So the symbol between 3 and 1 is : and it is the sign for ratio. The ratio is the number which can be used to express one quantity as a fraction of the other ones. Also units should be similar while comparing two things. We in a hurry can make a mistake in solving equation (3) and hence we need to be careful while doing this step.