Study the following information given in the paragraph and answer the questions accordingly. Following information gives data regarding number of persons in a village who plays different sports i.e. Cricket, Football and Hockey. Each person plays at least one sports. There are total 800 persons in a village who plays sports. 43 % of the total persons plays Cricket, 52.5 % of the total persons plays football and 55 % of the total persons plays Hockey. 96 persons plays both cricket and football but not Hockey. 100 persons plays both cricket and Hockey but not Football, 88 players plays both Hockey and Football but not cricket and 60 persons plays all the three sports.

What is the percentage of persons who play at least two sports?

Question

Study the following information given in the paragraph and answer the questions accordingly. Following information gives data regarding number of persons in a village who plays different sports i.e. Cricket, Football and Hockey. Each person plays at least one sports. There are total 800 persons in a village who plays sports. 43 % of the total persons plays Cricket, 52.5 % of the total persons plays football and 55 % of the total persons plays Hockey. 96 persons plays both cricket and football but not Hockey. 100 persons plays both cricket and Hockey but not Football, 88 players plays both Hockey and Football but not cricket and 60 persons plays all the three sports.

What is the percentage of persons who play at least two sports?

Accepted Answer

**Solution:**

1. Total persons = 800

2. Persons playing Cricket (C) = 43\% of 800 = $0.43 \times 800 = 344$

3. Persons playing Football (F) = 52.5\% of 800 = $0.525 \times 800 = 420$

4. Persons playing Hockey (H) = 55\% of 800 = $0.55 \times 800 = 440$

6. We need to find the percentage of persons who play at least two sports. This includes:
   - Those who play exactly two sports: 96 + 100 + 88 = 284
   - Those who play all three sports: 60

7. Total persons playing at least two sports = 284 + 60 = 344

8. Percentage = $\frac{344}{800} \times 100 = 43\%$

**Note:** The above calculation shows 43\%, but the options include 47\% as correct. Let's verify the total number of persons playing at least two sports carefully.

**Rechecking:**

- Total playing Cricket = 344
- Total playing Football = 420
- Total playing Hockey = 440

Sum of individual sports = 344 + 420 + 440 = 1204

Sum of exactly two sports = 96 + 100 + 88 = 284

Number playing all three = 60

Using the formula for union of three sets:

$$
|C \cup F \cup H| = |C| + |F| + |H| - |C \cap F| - |F \cap H| - |C \cap H| + |C \cap F \cap H|
$$

Where:

- $|C \cap F| = 96 + 60 = 156$
- $|F \cap H| = 88 + 60 = 148$
- $|C \cap H| = 100 + 60 = 160$

Plugging in values:

$$
800 = 344 + 420 + 440 - 156 - 148 - 160 + 60
$$

Calculate:

$$
800 = 1204 - 464 + 60 = 1204 - 404 = 800
$$

This confirms the data is consistent.

Now, persons playing at least two sports = persons playing exactly two sports + persons playing all three = 284 + 60 = 344

Percentage = $\frac{344}{800} \times 100 = 43\%$

**Answer:** 43\%

**Correction:** The correct answer is option (b) 43\%.

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