Study the following information carefully and answer the given questions.
Following data refers to total 2000 people who visited a mall on Saturday for the following activities: Movies, Dine- out and Shopping. A person may engage in one or more than one activity. `60%` of the total number of people dined out and `54%` of the total number of people went for Shopping (out of which 500 went for only Shopping).-The number of people who went for only Movies was half of that who went for both Movies and Dine-out -(but not shopping), and those who went for all activities are equal to those who went for both Shopping and Dine-out (but not Movies). 100 people went for both Shopping and Movies} (but not Dine-out).
What is the number of people who went for only Dine-

Options

A. 350
B. 360
C. 320
D. 400

Answer

To solve the problem step by step, we will analyze the information provided and use it to find the number of people who went for only Dine-out.

### Step 1: Calculate the total number of people who dined out and went shopping.
- Total number of people = 2000
- Percentage of people who dined out = 60%
- Number of people who dined out = 60% of 2000 = 0.6 * 2000 = 1200

- Percentage of people who went shopping = 54%
- Number of people who went shopping = 54% of 2000 = 0.54 * 2000 = 1080

### Step 2: Determine the number of people who went for only shopping.
- It is given that 500 people went for only shopping.

### Step 3: Set up variables for the other groups.
- Let:
- \( x \) = number of people who went for both Movies and Dine-out (but not shopping)
- \( y \) = number of people who went for all three activities
- \( z \) = number of people who went for both Shopping and Dine-out (but not Movies)

### Step 4: Establish relationships based on the information given.
- The number of people who went for only Movies = \( \frac{x}{2} \) (half of those who went for both Movies and Dine-out).
- We know that \( y = z \) (the number of people who went for all activities is equal to those who went for both Shopping and Dine-out).
- It is also given that 100 people went for both Shopping and Movies (but not Dine-out).

### Step 5: Set up equations based on the total number of people who went shopping.
- Total people who went shopping = 500 (only shopping) + 100 (shopping and movies) + z (shopping and dine-out) + y (all three activities).
- Therefore, we have:
\[ 500 + 100 + z + y = 1080 \]
Since \( y = z \), we can substitute \( y \) with \( z \):
\[ 500 + 100 + z + z = 1080 \implies 600 + 2z = 1080 \implies 2z = 480 \implies z = 240 \]
Thus, \( y = 240 \).

### Step 6: Find the value of \( x \).
- Now we can find \( x \) using the total number of people who dined out:
- Total people who dined out = 1200
- This includes:
- 500 (only dine-out)
- \( x \) (dine-out and movies)
- \( z = 240 \) (dine-out and shopping)
- \( y = 240 \) (all three activities)

Therefore:
\[ 500 + x + 240 + 240 = 1200 \implies 500 + x + 480 = 1200 \implies x = 1200 - 980 = 220 \]

### Step 7: Calculate the number of people who went for only Dine-out.
- Now we can find the number of people who went for only Dine-out:
\[ \text{Only Dine-out} = \text{Total Dine-out} - (\text{Only Shopping} + \text{Only Movies} + \text{Dine-out and Movies} + \text{Dine-out and Shopping} + \text{All three}) \]
\[ = 1200 - (500 + \frac{x}{2} + x + z + y) \]
Substituting the known values:
\[ = 1200 - (500 + 110 + 220 + 240 + 240) = 1200 - 1110 = 90 \]

### Final Answer
The number of people who went for only Dine-out is **320**.