The number of boys in a bus at the starting point is twice the number of girls. On the way when 15 boys got down and 10 girls entered the bus, the number of boys and girls became equal. How many boys were there at the start of the journey?

Options

A. 45
B. 40
C. 50
D. 55

Answer

To solve the problem step by step, let's define the variables and set up the equations based on the information given in the question.

### Step 1: Define the Variables
Let the number of girls in the bus at the starting point be \( x \). According to the problem, the number of boys is twice the number of girls. Therefore, the number of boys can be expressed as:
\[ \text{Number of boys} = 2x \]

### Step 2: Set Up the Situation After Changes
On the way, 15 boys get down from the bus, and 10 girls enter the bus. After these changes, the number of boys and girls becomes equal.

The new number of boys after 15 boys get down is:
\[ \text{New number of boys} = 2x - 15 \]

The new number of girls after 10 girls enter is:
\[ \text{New number of girls} = x + 10 \]

### Step 3: Set Up the Equation
According to the problem, after the changes, the number of boys equals the number of girls:
\[ 2x - 15 = x + 10 \]

### Step 4: Solve the Equation
Now, we will solve for \( x \):
1. Subtract \( x \) from both sides:
\[ 2x - x - 15 = 10 \]
This simplifies to:
\[ x - 15 = 10 \]

2. Add 15 to both sides:
\[ x = 25 \]

### Step 5: Find the Number of Boys
Now that we have the value of \( x \) (the number of girls), we can find the number of boys:
\[ \text{Number of boys} = 2x = 2 \times 25 = 50 \]

### Conclusion
The number of boys at the start of the journey was **50**.

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