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19 boys turn out for playing hockey. Of these, 11 are wearing hockey shirts and 14 are wearing hockey pants. There are no boys without shirts and/ or pants. What is the number of boys wearing full uniform?
- a)3
- b)5
- c)6
- d)8
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
19 boys turn out for playing hockey. Of these, 11 are wearing hockey s...
C is the correct option.If that is the case, then let the number of boys turning in proper jerseys and proper shorts be “x”.
Eleven boys are wearing proper jerseys, but they may not be wearing proper shorts.
Therefore, the number of boys wearing only proper jerseys = 11-x.
Similarly, the number of boys wearing only proper shorts = 14 - x.
Total number of boys = Number of boys wearing only proper jerseys + number of boys wearing only proper shorts + number of boys wearing both proper jerseys and proper shorts.
Therefore, 19 = (11-x) + (14-x) + x
So, 19 = 25 - x
So, x = 6
Eleven boys are wearing proper jerseys, but they may not be wearing proper shorts.
Therefore, the number of boys wearing only proper jerseys = 11-x.
Similarly, the number of boys wearing only proper shorts = 14 - x.
Total number of boys = Number of boys wearing only proper jerseys + number of boys wearing only proper shorts + number of boys wearing both proper jerseys and proper shorts.
Therefore, 19 = (11-x) + (14-x) + x
So, 19 = 25 - x
So, x = 6
Most Upvoted Answer
19 boys turn out for playing hockey. Of these, 11 are wearing hockey s...
Given information:
- Total number of boys = 19
- Number of boys wearing hockey shirts = 11
- Number of boys wearing hockey pants = 14
To find:
- Number of boys wearing a full uniform
Analysis:
- Let's assume that there are 'x' boys wearing both shirts and pants.
- Since there are no boys without shirts and/or pants, all the boys must fall into one of the following categories:
1. Boys wearing shirts only
2. Boys wearing pants only
3. Boys wearing both shirts and pants
Finding the number of boys in each category:
- Number of boys wearing shirts only = Total number of boys wearing shirts - Number of boys wearing both shirts and pants
= 11 - x
- Number of boys wearing pants only = Total number of boys wearing pants - Number of boys wearing both shirts and pants
= 14 - x
Total number of boys = Number of boys wearing shirts only + Number of boys wearing pants only + Number of boys wearing both shirts and pants
19 = 11 - x + 14 - x + x
19 = 25 - x
x = 25 - 19
x = 6
Therefore, there are 6 boys wearing both shirts and pants, which means there are 6 boys wearing a full uniform.
Hence, the correct answer is option C) 6.
- Total number of boys = 19
- Number of boys wearing hockey shirts = 11
- Number of boys wearing hockey pants = 14
To find:
- Number of boys wearing a full uniform
Analysis:
- Let's assume that there are 'x' boys wearing both shirts and pants.
- Since there are no boys without shirts and/or pants, all the boys must fall into one of the following categories:
1. Boys wearing shirts only
2. Boys wearing pants only
3. Boys wearing both shirts and pants
Finding the number of boys in each category:
- Number of boys wearing shirts only = Total number of boys wearing shirts - Number of boys wearing both shirts and pants
= 11 - x
- Number of boys wearing pants only = Total number of boys wearing pants - Number of boys wearing both shirts and pants
= 14 - x
Total number of boys = Number of boys wearing shirts only + Number of boys wearing pants only + Number of boys wearing both shirts and pants
19 = 11 - x + 14 - x + x
19 = 25 - x
x = 25 - 19
x = 6
Therefore, there are 6 boys wearing both shirts and pants, which means there are 6 boys wearing a full uniform.
Hence, the correct answer is option C) 6.
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