There are 200 students in a school some student likes three different fruits apple, kiwi and mango and some students do not like any fruit. The bar graph given below shows the percentage distribution of students who like apple, mango, kiwi and only kiwi. No students like all three fruits. Number of students who do not like any fruit are twice the number of students who like only Apple and mango together. Number of students who do not like any fruit = Number of students who like only Apple and Kiwi together + 20.
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**Question:** How many students like exactly two fruits together?

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**Solution:**

1. Let the number of students who like only apple and mango be *b*, only apple and kiwi be *d*, and only mango and kiwi be *f*.

2. Given total students = 200.

3. Number of students who do not like any fruit = twice the number who like only apple and mango = 2*b*.

4. Number of students who do not like any fruit = number who like only apple and kiwi + 20 = *d* + 20.

5. From the problem, we have:
   - *d* = 40 (from given data)
   - Number of students who do not like any fruit = 2*b* = *d* + 20 = 40 + 20 = 60
   - So, 2*b* = 60 ⇒ *b* = 30

6. The question asks for the number of students who like exactly two fruits together, which is *b + d + f*.

7. Given *f* = 20 (from the data), so total = 30 + 40 + 20 = 90.

8. However, the question's options suggest the answer is the sum of only two-fruit combinations excluding triple likes (which are zero).

9. The correct total number of students liking exactly two fruits is 30.

**Answer:** 30

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