Read the following information carefully and answer the questions given below-
1000 students appeared in an examination Out of which 275 students passed in physics, 320 students passed in chemistry and 350 students passed in mathematics. 84 students passed in both chemistry and mathematics 60 students passed in both physics and mathematics, 50 students passed in both physics and chemistry and 34 students passed in all the three subjects.
What is the ratio of students passed in physics and mathematics to the number of students passed in physics and chemistry?

Options

A. A) `5:6`
B. B) `2:3`
C. C) `6:5`
D. D) `3:2`

Answer

To solve the problem, we need to determine the number of students who passed in physics and mathematics, and the number of students who passed in physics and chemistry. Then, we will find the ratio of these two quantities.

### Step-by-Step Solution:

1. **Identify the number of students who passed in physics and mathematics:**
- From the information provided, we know that 60 students passed in both physics and mathematics.

2. **Identify the number of students who passed in physics and chemistry:**
- From the information provided, we know that 50 students passed in both physics and chemistry.

3. **Calculate the ratio of students passed in physics and mathematics to the number of students passed in physics and chemistry:**
- We have:
- Students passed in physics and mathematics = 60
- Students passed in physics and chemistry = 50
- Therefore, the ratio can be calculated as:
\[ \text{Ratio} = \frac{\text{Students passed in Physics and Mathematics}}{\text{Students passed in Physics and Chemistry}} = \frac{60}{50} \]

4. **Simplify the ratio:**
- Simplifying \(\frac{60}{50}\):
\[ \frac{60}{50} = \frac{6}{5} \]
- Thus, the ratio of students passed in physics and mathematics to those passed in physics and chemistry is \(6:5\).

### Final Answer:
The ratio of students passed in physics and mathematics to the number of students passed in physics and chemistry is \(6:5\).

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