In a college there are total 250 students. Average weight of boys is 50 and average weight of girls is 45. Also it is known that the overall average is 48. What is the number of boys in the college?

Options

A. A)150
B. B)100
C. C)125
D. D)200

Answer

To solve the problem step by step, we can use the method of allegation to find the number of boys in the college.

### Step 1: Understand the given data
- Total number of students = 250
- Average weight of boys = 50 kg
- Average weight of girls = 45 kg
- Overall average weight = 48 kg

### Step 2: Set up the allegation
We can set up the allegation to find the ratio of boys to girls based on their average weights and the overall average weight.

- The difference between the boys' average and the overall average:
\[ 50 - 48 = 2 \]

- The difference between the girls' average and the overall average:
\[ 48 - 45 = 3 \]

### Step 3: Determine the ratio of boys to girls
Using the differences calculated:
- The ratio of boys to girls is given by the differences:
\[ \text{Boys : Girls} = 3 : 2 \]

### Step 4: Calculate the total parts in the ratio
The total parts in the ratio of boys to girls is:
\[ 3 + 2 = 5 \]

### Step 5: Find the number of boys and girls
Now, we can find the number of boys and girls based on the total number of students (250):
- Number of boys:
\[ \text{Number of boys} = \left(\frac{3}{5}\right) \times 250 = 150 \]

- Number of girls:
\[ \text{Number of girls} = \left(\frac{2}{5}\right) \times 250 = 100 \]

### Conclusion
The number of boys in the college is **150**.

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