What is the ratio of the number of students studying science of colleges A and B together to the number of students studying commerce incolleges D and E together?

Options

A. `26:21`
B. `23:15`
C. `13:8`
D. `26:17`

Answer

To solve the question, we need to find the ratio of the number of students studying science in colleges A and B together to the number of students studying commerce in colleges D and E together. Here’s how we can do it step by step:

### Step 1: Identify the number of students studying science in colleges A and B
From the data provided:
- Number of students studying science in college A = 300
- Number of students studying science in college B = 350

Now, we will add these two numbers together:
\[ \text{Total students studying science in A and B} = 300 + 350 = 650 \]

### Step 2: Identify the number of students studying commerce in colleges D and E
From the data provided:
- Number of students studying commerce in college D = 275
- Number of students studying commerce in college E = 250

Now, we will add these two numbers together:
\[ \text{Total students studying commerce in D and E} = 275 + 250 = 525 \]

### Step 3: Calculate the ratio of students studying science in A and B to students studying commerce in D and E
Now we need to find the ratio of the total number of students studying science in colleges A and B to the total number of students studying commerce in colleges D and E:
\[ \text{Ratio} = \frac{\text{Total students studying science in A and B}}{\text{Total students studying commerce in D and E}} = \frac{650}{525} \]

### Step 4: Simplify the ratio
To simplify the ratio \( \frac{650}{525} \), we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 650 and 525 is 25.

\[ \frac{650 \div 25}{525 \div 25} = \frac{26}{21} \]

### Final Answer
Thus, the ratio of the number of students studying science in colleges A and B together to the number of students studying commerce in colleges D and E together is:
\[ \text{Ratio} = 26:21 \]

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