What is the ratio of the total number of students studying Science from institutes `C` and `D` together to the total number of students studying Computer Science from these two institutes together?

Options

A. `13 : 12`
B. `12 : 13`
C. `13 : 15`
D. `15 : 13`

Answer

To solve the problem, we need to find the ratio of the total number of students studying Science from institutes C and D together to the total number of students studying Computer Science from these two institutes together.

### Step-by-Step Solution:

1. **Identify the number of students studying Science in institutes C and D:**
- From the data provided, the number of students studying Science in institute C is 360.
- The number of students studying Science in institute D is 420.
- Therefore, the total number of students studying Science from both institutes is:
\[ \text{Total Science Students} = 360 + 420 = 780 \]

2. **Identify the number of students studying Computer Science in institutes C and D:**
- The number of students studying Computer Science in institute C is 380.
- The number of students studying Computer Science in institute D is 340.
- Therefore, the total number of students studying Computer Science from both institutes is:
\[ \text{Total Computer Science Students} = 380 + 340 = 720 \]

3. **Calculate the ratio of total Science students to total Computer Science students:**
- The ratio can be expressed as:
\[ \text{Ratio} = \frac{\text{Total Science Students}}{\text{Total Computer Science Students}} = \frac{780}{720} \]

4. **Simplify the ratio:**
- To simplify the ratio, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 780 and 720 is 60.
- Therefore, we simplify the ratio as follows:
\[ \frac{780 \div 60}{720 \div 60} = \frac{13}{12} \]

5. **Final Answer:**
- The ratio of the total number of students studying Science from institutes C and D together to the total number of students studying Computer Science from these two institutes together is:
\[ \text{Ratio} = 13 : 12 \]