A basket contains only four kinds of fruits -guavas mangoes ,oranges and pears .What is the minimum number of fruits that should be picked from the basket to ensure that at least 5 guavas or at least 6 mangoes or at least 7 organges or at least 8 pears are picked ?

Options

A. 25
B. 26
C. 24
D. 23

Answer

To solve the problem, we need to determine the minimum number of fruits that must be picked from the basket to ensure that at least 5 guavas, or at least 6 mangoes, or at least 7 oranges, or at least 8 pears are picked.

### Step-by-Step Solution:

1. **Identify the conditions**: We need to ensure that we have at least:
- 5 guavas
- 6 mangoes
- 7 oranges
- 8 pears

2. **Calculate the maximum number of fruits we can pick without meeting any of the conditions**:
- For guavas, if we pick 4 (which is one less than 5), we have: **4 guavas**
- For mangoes, if we pick 5 (which is one less than 6), we have: **5 mangoes**
- For oranges, if we pick 6 (which is one less than 7), we have: **6 oranges**
- For pears, if we pick 7 (which is one less than 8), we have: **7 pears**

3. **Sum these maximum counts**:
- Total fruits picked without meeting any condition = 4 (guavas) + 5 (mangoes) + 6 (oranges) + 7 (pears)
- Calculation: \( 4 + 5 + 6 + 7 = 22 \)

4. **Determine the minimum number of fruits to ensure at least one condition is met**:
- Since we can pick 22 fruits without satisfying any of the conditions, we need to pick one more fruit to ensure that at least one condition is satisfied.
- Therefore, the minimum number of fruits to be picked = \( 22 + 1 = 23 \)

### Final Answer:
The minimum number of fruits that should be picked from the basket to ensure that at least 5 guavas or at least 6 mangoes or at least 7 oranges or at least 8 pears are picked is **23**.

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