The ratio of boys and girls in a college was 5 : 4. New students admitted and the number of boys went up by 20% and the number of girls went up by 50%. What is the new ratio of boys and girls in the college?
(a)`1 : 2 `
(b)`2 : 3 `
(c)`1 : 1 `
(d)`3 : 4`

Options

A. `1 : 2 `
B. `2 : 3 `
C. `1 : 1 `
D. `3 : 4`

Answer

To find the new ratio of boys and girls in the college after the increase in their numbers, we can follow these steps:

### Step 1: Define the initial numbers of boys and girls
Let the initial number of boys be \( 5x \) and the initial number of girls be \( 4x \), where \( x \) is a common multiplier.

### Step 2: Calculate the increase in the number of boys
The number of boys increased by 20%. Therefore, the new number of boys can be calculated as:
\[ \text{New number of boys} = 5x + 0.2 \times 5x = 5x \times (1 + 0.2) = 5x \times 1.2 = 6x \]

### Step 3: Calculate the increase in the number of girls
The number of girls increased by 50%. Therefore, the new number of girls can be calculated as:
\[ \text{New number of girls} = 4x + 0.5 \times 4x = 4x \times (1 + 0.5) = 4x \times 1.5 = 6x \]

### Step 4: Find the new ratio of boys to girls
Now, we have the new number of boys as \( 6x \) and the new number of girls as \( 6x \). The new ratio of boys to girls is:
\[ \text{New ratio} = \frac{6x}{6x} = 1:1 \]

### Conclusion
Thus, the new ratio of boys to girls in the college is \( 1:1 \).