Question

A bus starts from city X. The number of women in the bus is half of the number of men. In city Y, 10 men leave the bus and five women enter. Now the number of men and women is equal. In the beginning, how many passengers entered the bus?

• A. 15
• B. 30
• C. 36
• D. 45

Hint:

When populations shift over time, write present counts first, then carefully apply the changes before setting up the equation—this avoids sign mistakes.

Answer 1

The Correct Option is D

Step 1: Define variables. 
Let present (initial) numbers be: men \(= m\), women \(= w\) with \(w = \dfrac{m}{2}\). 

Step 2: Use the condition after the stop at Y. 
At Y: men \(= m-10\), women \(= w+5\). 
Equality there gives \(m - 10 = w + 5 \Rightarrow m - w = 15\). 

Step 3: Solve the system. 
Since \(w = \dfrac{m}{2}\), we have \(m - \dfrac{m}{2} = 15 \Rightarrow \dfrac{m}{2} = 15 \Rightarrow m = 30\). 
Hence \(w = \dfrac{m}{2} = 15\). 

Step 4: Conclude total initially. 
Initial passengers \(= m + w = 30 + 15 = \boxed{45}\).