In year 2016, ratio of boys to girls in a school is `36:19` And in year 2017, number of boys is increased by 1440 and number of girls is increased by `15%` if in 2017, there were total increase in the number of students is 1725 then find the increased number of boys in the school.

Options

A. 7240
B. 5440
C. 6040
D. 5040

Answer

To solve the problem step by step, let's break it down:

### Step 1: Determine the total number of boys and girls in 2016
The ratio of boys to girls in 2016 is given as 36:19. Let's assume the number of boys is 36x and the number of girls is 19x.

### Step 2: Calculate the total increase in students from 2016 to 2017
In 2017, the number of boys increased by 1440, and the number of girls increased by 15%. The total increase in the number of students is given as 1725.

### Step 3: Set up the equation for the increase in girls
Let’s denote the number of girls in 2016 as 19x. The increase in the number of girls is 15% of 19x:
\[ \text{Increase in girls} = 0.15 \times 19x = 2.85x \]

### Step 4: Write the equation for total increase in students
The total increase in students is the sum of the increase in boys and girls:
\[ 1440 + 2.85x = 1725 \]

### Step 5: Solve for x
Now, we can solve for x:
\[ 2.85x = 1725 - 1440 \]
\[ 2.85x = 285 \]
\[ x = \frac{285}{2.85} = 100 \]

### Step 6: Calculate the number of boys and girls in 2016
Now that we have x, we can find the number of boys and girls:
- Number of boys in 2016:
\[ \text{Boys} = 36x = 36 \times 100 = 3600 \]
- Number of girls in 2016:
\[ \text{Girls} = 19x = 19 \times 100 = 1900 \]

### Step 7: Calculate the total number of boys in 2017
In 2017, the number of boys increased by 1440:
\[ \text{Total boys in 2017} = 3600 + 1440 = 5040 \]

### Conclusion
The increased number of boys in the school is **5040**.

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