There are 4 qualifying examinations to enter into Oxford University: RAT, BAT, SAT, and PAT. An Engineer cannot go to Oxford University through BAT or SAT. A CA on the other hand can go to the Oxford University through the RAT,BAT & PAT but not through SAT. Further there are 3 ways to become a CA(viz., Foundation, Inter & Final). Find the ratio of number of ways in which an Engineer can make it to Oxford University to the number of ways a CA can make it to Oxford University.

Options

A. `3:2`
B. `2 :3`
C. `2 :9`
D. `9 :2`

Answer

To solve the problem step by step, let's analyze the information given and calculate the number of ways for both Engineers and CAs to qualify for Oxford University.

### Step 1: Identify the qualifying examinations
The qualifying examinations are:
- RAT
- BAT
- SAT
- PAT

### Step 2: Determine the options for Engineers
According to the problem, Engineers cannot go to Oxford University through BAT or SAT. Therefore, the only options available for Engineers are:
- RAT
- PAT

Thus, the number of ways for an Engineer to qualify for Oxford University is:
- **Number of ways for Engineers = 2 (RAT and PAT)**

### Step 3: Determine the options for CAs
The problem states that CAs can go to Oxford University through RAT, BAT, and PAT, but not through SAT. Therefore, the options available for CAs are:
- RAT
- BAT
- PAT

Thus, the number of ways for a CA to qualify for Oxford University is:
- **Number of ways for CAs = 3 (RAT, BAT, and PAT)**

### Step 4: Calculate the ratio of ways
Now, we need to find the ratio of the number of ways an Engineer can make it to Oxford University to the number of ways a CA can make it to Oxford University.

The ratio can be calculated as follows:
\[ \text{Ratio} = \frac{\text{Number of ways for Engineers}}{\text{Number of ways for CAs}} = \frac{2}{3} \]

### Final Answer
The ratio of the number of ways in which an Engineer can make it to Oxford University to the number of ways a CA can make it to Oxford University is:
\[ \text{Ratio} = 2:3 \]

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