Out of 500 car drivers, 400 are the owners of Maruti and 200 are the owners of Hundai. If 50 are the owners of both, then find the whether the datas are correct or not ?

Answer

To determine whether the data provided about car drivers is correct, we can use the principle of inclusion-exclusion. Let's break down the solution step by step.

### Step 1: Identify the given data
- Total number of car drivers (N) = 500
- Number of Maruti owners (NM) = 400
- Number of Hyundai owners (NH) = 200
- Number of drivers owning both Maruti and Hyundai (N(M ∩ H)) = 50

### Step 2: Apply the principle of inclusion-exclusion
To find the total number of unique drivers who own either Maruti or Hyundai or both, we use the formula:

\[ N(M \cup H) = N(M) + N(H) - N(M \cap H) \]

Where:
- \(N(M \cup H)\) = Total number of drivers who own either Maruti or Hyundai
- \(N(M)\) = Number of Maruti owners
- \(N(H)\) = Number of Hyundai owners
- \(N(M \cap H)\) = Number of drivers who own both

### Step 3: Substitute the values into the formula
Substituting the values we have:

\[ N(M \cup H) = 400 + 200 - 50 \]

### Step 4: Calculate the total
Now, calculate the total:

\[ N(M \cup H) = 400 + 200 - 50 = 550 \]

### Step 5: Compare with the total number of drivers
We found that the total number of unique drivers who own either Maruti or Hyundai is 550. However, we were given that there are only 500 drivers in total.

### Step 6: Conclusion
Since 550 (the calculated total) is greater than 500 (the given total), the data provided is not correct.

### Final Answer
The given data is not correct.

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