Question

When a bus started from the first stop, the number of male passengers to the number of female passengers was 3:1. At the first stop, 16 passengers got down and 6 more female passengers got in. The ratio of the male to the female passenger now becomes 2:1. What was the total number of passengers in the bus when it started from the first stop?

Answer 1

Hint: For this question we have to let the common factor as x then we will try to form equations on x using the given statements and finally the total number of males when the bus started is 3x and the female passengers is x so the total passenger will be 4x. Therefore we need to find the value of 4x

Complete step by step solution:
Let us consider that x is the common factor in the ratio 3:1.
In this case the total number of male passengers will become 3x and the total number of female passengers will become x
Hence the total number of passengers will become \[3x + x = 4x\]
At the first stop 16 passengers got down and 6 females passengers got up
Therefore the total number of male passengers left is \[\left( {4x - 16} \right) \times \dfrac{3}{4} = 3x - 12\]
For female passengers this becomes \[\left( {4x - 16} \right) \times \dfrac{1}{4} + 6 = x + 2\]
So now we have the ratio after the first stop as 2:1 also we can make another ratio of male:female after first stop in terms of x which will become \[3x - 12:x + 2\]
Now these two ratios must satisfy each other;
\[\begin{array}{l}
\therefore \dfrac{{3x - 12}}{{x + 2}} = \dfrac{2}{1}\\
 \Rightarrow 3x - 12 = 2\left( {x + 2} \right)\\
 \Rightarrow 3x - 2x = 12 + 4\\
 \Rightarrow x = 16
\end{array}\]
Also we have noted that the total number of passengers is nothing but 4x, which means \[4x = 4 \times 16 = 64\]

Note: We knew that the total number of passengers in the bus was 4x and the total number of male passengers in the bus was 3x and the female passengers were x initially thats why while getting the new ratio in male passengers i have multiplied it with \[\dfrac{3}{4}\] and for female passengers it was \[\dfrac{1}{4}\] .