In a class 80 students the boys and girls are in the ratio of 5 : 3. The students can speak only Hindi or Engish or both Hindi and English. The number of boys and the number of girls who can speak only Hindi is equal and each of them is 40% of the total number of girls. 10% of the girls can speak both the languages and 58% of the boys can speak only English
What percentage of boys and girls can speak only Hindi?

Options

A. 24
B. 40
C. 50
D. 30

Answer

To solve the problem step by step, we will break down the information given and perform the necessary calculations.

### Step 1: Determine the number of boys and girls in the class
The ratio of boys to girls is given as 5:3. The total number of students is 80.

- Let the number of boys be \(5x\) and the number of girls be \(3x\).
- Therefore, \(5x + 3x = 80\).
- This simplifies to \(8x = 80\).
- Solving for \(x\), we get \(x = 10\).

Now, we can find the number of boys and girls:
- Number of boys = \(5x = 5 \times 10 = 50\)
- Number of girls = \(3x = 3 \times 10 = 30\)

### Step 2: Find the number of boys and girls who can speak only Hindi
We know that the number of boys who can speak only Hindi is equal to the number of girls who can speak only Hindi, and each of them is 40% of the total number of girls.

- Number of girls who can speak only Hindi = \(40\% \text{ of } 30 = \frac{40}{100} \times 30 = 12\).
- Therefore, the number of boys who can speak only Hindi = 12 (since they are equal).

### Step 3: Find the number of girls who can speak both languages
It is given that 10% of the girls can speak both languages.

- Number of girls who can speak both languages = \(10\% \text{ of } 30 = \frac{10}{100} \times 30 = 3\).

### Step 4: Find the number of boys who can speak only English
It is given that 58% of the boys can speak only English.

- Number of boys who can speak only English = \(58\% \text{ of } 50 = \frac{58}{100} \times 50 = 29\).

### Step 5: Calculate the total number of students who can speak only Hindi
Now we can summarize the number of students who can speak only Hindi:
- Boys who can speak only Hindi = 12
- Girls who can speak only Hindi = 12

Total students who can speak only Hindi = \(12 + 12 = 24\).

### Step 6: Calculate the percentage of students who can speak only Hindi
To find the percentage of students who can speak only Hindi, we use the formula:

\[ \text{Percentage} = \left(\frac{\text{Number of students who speak only Hindi}}{\text{Total number of students}}\right) \times 100 \]

Substituting the values:

\[ \text{Percentage} = \left(\frac{24}{80}\right) \times 100 = 30\% \]

### Final Answer
The percentage of boys and girls who can speak only Hindi is **30%**.

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