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In a town, 48% people are educated, 51% people are young and 60% are servicemen. 24% are educated and young, 25% are young and servicemen, 27% are educated and servicemen and 5% have all the qualities. If the total number of persons in this town is 300, what is the ratio of those who have exactly two characteristics and those who have only one characteristic?
- a)31/22
- b)47/61
- c)61/47
- d)None of these
Correct answer is option 'D'. Can you explain this answer?
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Understanding the Problem
In this problem, we need to analyze the characteristics of people in a town with a total population of 300. The population has three characteristics: educated, young, and servicemen.
Given Data
- Total population: 300
- Percentage of educated: 48%
- Percentage of young: 51%
- Percentage of servicemen: 60%
- Educated and young: 24%
- Young and servicemen: 25%
- Educated and servicemen: 27%
- All three characteristics: 5%
Calculating Actual Numbers
- Total educated = 48% of 300 = 144
- Total young = 51% of 300 = 153
- Total servicemen = 60% of 300 = 180
- Educated and young = 24% of 300 = 72
- Young and servicemen = 25% of 300 = 75
- Educated and servicemen = 27% of 300 = 81
- All three = 5% of 300 = 15
Using Inclusion-Exclusion Principle
To find those with exactly two characteristics, we can use the formula:
- Only Educated & Young = (Educated and Young) - (All three) = 72 - 15 = 57
- Only Young & Servicemen = (Young and Servicemen) - (All three) = 75 - 15 = 60
- Only Educated & Servicemen = (Educated and Servicemen) - (All three) = 81 - 15 = 66
Total with Exactly Two Characteristics
- Total with exactly two characteristics = 57 + 60 + 66 = 183
Calculating Those with Only One Characteristic
Using the totals calculated earlier:
- Only Educated = Total Educated - (Only Educated & Young + Only Educated & Servicemen + All three)
= 144 - (57 + 66 + 15) = 6
- Only Young = Total Young - (Only Educated & Young + Only Young & Servicemen + All three)
= 153 - (57 + 60 + 15) = 21
- Only Servicemen = Total Servicemen - (Only Educated & Servicemen + Only Young & Servicemen + All three)
= 180 - (66 + 60 + 15) = 39
Total with Only One Characteristic
- Total with only one characteristic = 6 + 21 + 39 = 66
Calculating the Ratio
- Ratio of exactly two characteristics to only one characteristic = 183 : 66 = 61 : 22
Thus, the ratio of those who have exactly two characteristics to those who have only one characteristic is not matching any options provided, leading us to conclude that the correct answer is option 'D'.
In this problem, we need to analyze the characteristics of people in a town with a total population of 300. The population has three characteristics: educated, young, and servicemen.
Given Data
- Total population: 300
- Percentage of educated: 48%
- Percentage of young: 51%
- Percentage of servicemen: 60%
- Educated and young: 24%
- Young and servicemen: 25%
- Educated and servicemen: 27%
- All three characteristics: 5%
Calculating Actual Numbers
- Total educated = 48% of 300 = 144
- Total young = 51% of 300 = 153
- Total servicemen = 60% of 300 = 180
- Educated and young = 24% of 300 = 72
- Young and servicemen = 25% of 300 = 75
- Educated and servicemen = 27% of 300 = 81
- All three = 5% of 300 = 15
Using Inclusion-Exclusion Principle
To find those with exactly two characteristics, we can use the formula:
- Only Educated & Young = (Educated and Young) - (All three) = 72 - 15 = 57
- Only Young & Servicemen = (Young and Servicemen) - (All three) = 75 - 15 = 60
- Only Educated & Servicemen = (Educated and Servicemen) - (All three) = 81 - 15 = 66
Total with Exactly Two Characteristics
- Total with exactly two characteristics = 57 + 60 + 66 = 183
Calculating Those with Only One Characteristic
Using the totals calculated earlier:
- Only Educated = Total Educated - (Only Educated & Young + Only Educated & Servicemen + All three)
= 144 - (57 + 66 + 15) = 6
- Only Young = Total Young - (Only Educated & Young + Only Young & Servicemen + All three)
= 153 - (57 + 60 + 15) = 21
- Only Servicemen = Total Servicemen - (Only Educated & Servicemen + Only Young & Servicemen + All three)
= 180 - (66 + 60 + 15) = 39
Total with Only One Characteristic
- Total with only one characteristic = 6 + 21 + 39 = 66
Calculating the Ratio
- Ratio of exactly two characteristics to only one characteristic = 183 : 66 = 61 : 22
Thus, the ratio of those who have exactly two characteristics to those who have only one characteristic is not matching any options provided, leading us to conclude that the correct answer is option 'D'.
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In a town, 48% people are educated, 51% people are young and 60% are servicemen. 24% are educated and young, 25% are young and servicemen, 27% are educated and servicemen and 5% have all the qualities. If the total number of persons in this town is 300, what is the ratio of those who have exactly two characteristics and those who have only one characteristic?a)31/22b)47/61c)61/47d)None of theseCorrect answer is option 'D'. Can you explain this answer?
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