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On a survey of 100 boys it was found that 50 used white that 50 used white shirt 40 red and 30 blue. 20 were habituated in using both white and red shirts 15 both red and blue shirts and 10 blue and white shirts. Find the number of boys using all the colours.
  • a)
    20
  • b)
    25
  • c)
    30
  • d)
    None
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
On a survey of 100 boys it was found that 50 used white that 50 used w...
Analysis:
To find the number of boys using all three colors (white, red, and blue), we need to use the principle of inclusion-exclusion.

Given Data:
- Boys using white shirts = 50
- Boys using red shirts = 40
- Boys using blue shirts = 30
- Boys using both white and red shirts = 20
- Boys using both red and blue shirts = 15
- Boys using both blue and white shirts = 10

Calculation:
Let's denote:
- Boys using all three colors as x
- Boys using only white and red = Boys using white - Boys using both white and red = 50 - 20 = 30
- Boys using only red and blue = Boys using red - Boys using both red and blue = 40 - 15 = 25
- Boys using only blue and white = Boys using blue - Boys using both blue and white = 30 - 10 = 20
Now, we can apply the principle of inclusion-exclusion:
Total boys using at least one color = Boys using white + Boys using red + Boys using blue - (Boys using white and red + Boys using red and blue + Boys using blue and white) + Boys using all three colors
100 = 50 + 40 + 30 - (20 + 15 + 10) + x
100 = 120 - 45 + x
x = 25
Therefore, the number of boys using all three colors (white, red, and blue) is 25. Hence, the correct answer is option B.
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On a survey of 100 boys it was found that 50 used white that 50 used white shirt 40 red and 30 blue. 20 were habituated in using both white and red shirts 15 both red and blue shirts and 10 blue and white shirts. Find the number of boys using all the colours.a)20b)25c)30d)NoneCorrect answer is option 'B'. Can you explain this answer?
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