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.

• A. 38
• B. 36
• C. 54
• D. None of the above

Hint:

Use inclusion-exclusion principle for three sets: \( A + B + C - (AB + BC + AC) + ABC \)

Answer 1

The Correct Option is C

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:

 \(\text{Total} = A + B + C - (A \cap B + B \cap C + A \cap C) + A \cap B \cap C = 42 + 34 + 20 - (24 + 10 + 12) + 4 = 96 - 46 + 4 = {54}\)