Question:
In a certain zoo, there are 42 animals in one sector, 34 in the second sector and 20 in the third sector. Out of this, 24 graze in sector one and also in sector two. 10 graze in sector two and sector three, 12 graze in sector one and sector three. These figures also include four animals grazing in all the three sectors are now transported to another zoo. Find the total number of animals.
In a certain zoo, there are 42 animals in one sector, 34 in the second sector and 20 in the third sector. Out of this, 24 graze in sector one and also in sector two. 10 graze in sector two and sector three, 12 graze in sector one and sector three. These figures also include four animals grazing in all the three sectors are now transported to another zoo. Find the total number of animals.
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Use inclusion-exclusion principle for three sets: \( A + B + C - (AB + BC + AC) + ABC \)
Updated On: Jul 29, 2025
- 38
- 36
- 54
- None of the above
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The Correct Option is C
Solution and Explanation
Use Venn diagram: Let A = 42, B = 34, C = 20 Let overlaps: \[ A \cap B = 24, \quad B \cap C = 10, \quad A \cap C = 12, \quad A \cap B \cap C = 4 \] Apply:
\(\text{Total} = A + B + C - (A \cap B + B \cap C + A \cap C) + A \cap B \cap C = 42 + 34 + 20 - (24 + 10 + 12) + 4 = 96 - 46 + 4 = {54}\)
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