In army `49%` of the soldiers speak Hindi `36%` of the soldiers speak english , `15%` of the soldiers speak both language. If `900` soldiers do not speak any of the language. Find how many soldiers speak only English.

Options

A. a) `430`
B. b) `620`
C. c) `630`
D. d) `530`

Answer

To solve the problem, we will use the information given about the percentages of soldiers who speak Hindi, English, both languages, and those who do not speak any language. We will also need to find the total number of soldiers in the army.

### Step-by-Step Solution:

1. **Define Variables:**
Let the total number of soldiers in the army be \( x \).

2. **Calculate Soldiers Speaking Hindi and English:**
- Soldiers speaking Hindi = \( 49\% \) of \( x \) = \( 0.49x \)
- Soldiers speaking English = \( 36\% \) of \( x \) = \( 0.36x \)
- Soldiers speaking both languages = \( 15\% \) of \( x \) = \( 0.15x \)

3. **Calculate Soldiers Speaking Only Hindi and Only English:**
- Soldiers speaking only Hindi = Soldiers speaking Hindi - Soldiers speaking both = \( 0.49x - 0.15x = 0.34x \)
- Soldiers speaking only English = Soldiers speaking English - Soldiers speaking both = \( 0.36x - 0.15x = 0.21x \)

4. **Calculate Total Soldiers Speaking Either Language:**
Using the principle of inclusion-exclusion, the total number of soldiers speaking at least one language is:
\[ \text{Total speaking at least one language} = (\text{Only Hindi}) + (\text{Only English}) + (\text{Both}) = 0.34x + 0.21x + 0.15x = 0.70x \]

5. **Calculate Soldiers Not Speaking Any Language:**
According to the problem, \( 900 \) soldiers do not speak any language. Therefore:
\[ \text{Total soldiers} - \text{Total speaking at least one language} = 900 \]
\[ x - 0.70x = 900 \]
\[ 0.30x = 900 \]

6. **Solve for Total Soldiers:**
\[ x = \frac{900}{0.30} = 3000 \]

7. **Calculate Soldiers Speaking Only English:**
Now that we have the total number of soldiers, we can find the number of soldiers who speak only English:
\[ \text{Soldiers speaking only English} = 0.21x = 0.21 \times 3000 = 630 \]

### Final Answer:
The number of soldiers who speak only English is **630**.

---