The numbers of students speaking English and Hindi are in the ratio of 4:5. If the number of students speaking English increased by ` 35%` and that speaking Hindi increased by ` 20%` , what would be the new respective ratio?

Options

A. `19 : 20`
B. ` 7 : 8`
C. ` 8 : 9`
D. ` 9 : 10`

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Define the initial ratio
The initial ratio of students speaking English to those speaking Hindi is given as 4:5.

Let:
- Number of students speaking English = 4x
- Number of students speaking Hindi = 5x

### Step 2: Calculate the increase in the number of students
Next, we need to calculate the new number of students after the respective increases.

1. **Increase in English**:
- Increase = 35% of (4x)
- Increase = (35/100) * 4x = 1.4x
- New number of students speaking English = 4x + 1.4x = 5.4x

2. **Increase in Hindi**:
- Increase = 20% of (5x)
- Increase = (20/100) * 5x = 1x
- New number of students speaking Hindi = 5x + 1x = 6x

### Step 3: Form the new ratio
Now, we can form the new ratio of students speaking English to those speaking Hindi:

New ratio = (New number of students speaking English) : (New number of students speaking Hindi)
New ratio = 5.4x : 6x

### Step 4: Simplify the new ratio
To simplify the ratio, we can divide both terms by x:

New ratio = 5.4 : 6

To make it easier to work with, we can multiply both terms by 10 to eliminate the decimal:

New ratio = 54 : 60

Now, we can simplify this ratio further by dividing both terms by 6:

New ratio = 9 : 10

### Final Answer
The new respective ratio of students speaking English to those speaking Hindi is **9:10**.

---