If the following venn diagram represents number of players in games (Cricket, Hockey and Football), then which of the following is percentage of players in a game whose number of players are 7 less than the Football game?
Show Hint
To divide by 91 quickly in your head, recognize that 18 out of 90 is exactly 20%. Since 91 is very close to 90, the result must be extremely close to 20%. This allows you to select the correct option instantly.
• Step 1: Understanding the Question: This question uses Venn diagrams and percentages. We must first understand the distribution of players, find the number of players in the Football game, determine the game having 7 fewer players, and calculate its percentage representation relative to the total number of players.
• Step 2: Key Formula or Approach:
1. Identify all individual values from the Venn diagram regions:
Hockey-only = 41
Football-only = 25
Cricket-only = 18
Intersection region = 7
2. Sum all values to find the total number of players (\(N_{\text{total}}\)).
3. Find the reference value (Football game = 25).
4. Find the targeted game value: \(25 - 7 = 18\) (which corresponds to Cricket).
5. Find the percentage of this targeted game:
\[ \text{Percentage} = \left(\frac{\text{Targeted Game Players}}{N_{\text{total}}}\right) \times 100 \]
• Step 3: Detailed Explanation:
- Let us sum all the disjoint regions representing the players to get the total headcount:
\[ N_{\text{total}} = 41 \text{ (Hockey)} + 18 \text{ (Cricket)} + 7 \text{ (Intersection)} + 25 \text{ (Football)} = 91 \]
- The number of players indicated in the Football region is 25.
- We are looking for the game whose player count is 7 less than Football:
\[ \text{Targeted count} = 25 - 7 = 18 \]
Comparing this value to the diagram, 18 corresponds to the Cricket game.
- Now, we compute the percentage of Cricket players out of the total pool of players:
\[ \text{Percentage of Cricket players} = \left(\frac{18}{91}\right) \times 100 \]
\[ \text{Percentage} \approx 0.1978 \times 100 \approx 19.78\% \]
This is extremely close to 20%. Thus, the approximate value is 20%.
• Step 4: Final Answer: The percentage of players in that game is approximately 20%, matching option (C).
