In a certain city of 15000 families, 3.5% of families who read A but not B look into advertisements, 25% of the families who read B but not A look into advertisements and 50% of the families, who read both A and B look into advertisements. It is known that 8000 families read A, 4000 read B and 1000 read both A and B. The Number of families who look into advertisements are

Options

A. a. 1295
B. b. 1395
C. c. 1495
D. d. 1500

Answer

To solve the problem, we will break it down step by step.

### Step 1: Identify the number of families in each category
We know:
- Total families = 15000
- Families reading A = 8000
- Families reading B = 4000
- Families reading both A and B = 1000

From this, we can find the number of families reading only A and only B.

**Families reading only A:**
\[ \text{Only A} = \text{Total A} - \text{Both A and B} = 8000 - 1000 = 7000 \]

**Families reading only B:**
\[ \text{Only B} = \text{Total B} - \text{Both A and B} = 4000 - 1000 = 3000 \]

### Step 2: Calculate the families looking into advertisements
We are given the following percentages:
- 3.5% of families who read A but not B look into advertisements.
- 25% of families who read B but not A look into advertisements.
- 50% of families who read both A and B look into advertisements.

**Families looking into advertisements from only A:**
\[ \text{Families from Only A} = 7000 \]
\[ \text{Looking into ads} = 3.5\% \text{ of } 7000 = \frac{3.5}{100} \times 7000 = 245 \]

**Families looking into advertisements from only B:**
\[ \text{Families from Only B} = 3000 \]
\[ \text{Looking into ads} = 25\% \text{ of } 3000 = \frac{25}{100} \times 3000 = 750 \]

**Families looking into advertisements from both A and B:**
\[ \text{Families from Both A and B} = 1000 \]
\[ \text{Looking into ads} = 50\% \text{ of } 1000 = \frac{50}{100} \times 1000 = 500 \]

### Step 3: Total families looking into advertisements
Now we can sum up all the families looking into advertisements:
\[ \text{Total looking into ads} = 245 + 750 + 500 = 1495 \]

### Final Answer
The number of families who look into advertisements is **1495**.

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