In a survey among B - school students , 68% of those surveyed were in favour of atleast one of the three magazines - A, B and C. 38% of those favoured , magazines - A, 26% favoured magazine B and 36% favoured magazine C . If 11% of those surveyed favoured more than one of the three magazine . What percent of those surveyed favoured more than one of the three magazines ?

Options

A. 0.25
B. 0.33
C. 0.21
D. 0.26

Answer

To solve the problem step by step, we will use the given percentages and apply the principle of inclusion-exclusion in set theory.

### Step 1: Understand the Information Given
We know:
- 68% of students favor at least one of the magazines (A, B, or C).
- 38% favor magazine A.
- 26% favor magazine B.
- 36% favor magazine C.
- 11% favor more than one magazine.

### Step 2: Set Up the Equations
Let:
- \( x \) = percentage of students who favor only magazine A.
- \( y \) = percentage of students who favor only magazine B.
- \( z \) = percentage of students who favor only magazine C.
- \( p \) = percentage of students who favor both A and B (but not C).
- \( q \) = percentage of students who favor both A and C (but not B).
- \( r \) = percentage of students who favor both B and C (but not A).
- \( s \) = percentage of students who favor all three magazines A, B, and C.

From the problem, we can set up the following equations based on the information provided:

1. \( x + y + z + p + q + r + s = 68 \) (total who favor at least one magazine)
2. \( x + p + q + s = 38 \) (total who favor magazine A)
3. \( y + p + r + s = 26 \) (total who favor magazine B)
4. \( z + q + r + s = 36 \) (total who favor magazine C)
5. \( p + q + r + s = 11 \) (those who favor more than one magazine)

### Step 3: Solve the Equations
We can use the fifth equation to express \( p + q + r + s \) in terms of the other variables. We know that \( p + q + r + s = 11 \).

Now we can substitute this into the first equation:

1. \( x + y + z + 11 = 68 \)
\[ x + y + z = 68 - 11 = 57 \]

### Step 4: Find the Percentage of Students Who Favor More Than One Magazine
From the fifth equation, we already know that 11% of students favor more than one magazine.

Thus, the percentage of students who favor more than one of the three magazines is:
\[ \text{Percentage} = 11\% \]

### Step 5: Conclusion
The answer to the question is that **11% of those surveyed favored more than one of the three magazines**.