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In a statistical investigation of 1003 families of Calcutta, it was found that 63 families has neither a radio nor a T.V, 794 families has a radio and 187 has T.V. The number of families in that group having both a radio and a T.V is
- a)36
- b)41
- c)32
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
In a statistical investigation of 1003 families of Calcutta, it was fo...
Let R be the set of families having a radio and T the set families having a T.V., then n (R ∪ T) = The number of families having at least on of the radio and T.V. = 1003 – 63 = 940 n(R) = 794 and n(T) = 187 Let x families have both a radio and a T.V.
Then number of families who have only radio = 794 – x
And the number of families who have only T.V. = 187 – x From Venn diagram, 794 – x + x – 187 – x = 940
⇒ 981 – x = 940 or x = 981 – 940 = 41 Hence, the required number of families having both a radio and a T.V. = 41
Most Upvoted Answer
In a statistical investigation of 1003 families of Calcutta, it was fo...
Given Information:
- Total number of families investigated = 1003
- Number of families with neither a radio nor a TV = 63
- Number of families with a radio = 794
- Number of families with a TV = 187
Calculating the number of families with both a radio and a TV:
To find the number of families that have both a radio and a TV, we need to subtract the number of families with neither a radio nor a TV from the total number of families.
Total number of families = Number of families with neither a radio nor a TV + Number of families with a radio + Number of families with a TV + Number of families with both a radio and a TV
1003 = 63 + 794 + 187 + Number of families with both a radio and a TV
Number of families with both a radio and a TV = 1003 - (63 + 794 + 187)
Number of families with both a radio and a TV = 1003 - 1044
Number of families with both a radio and a TV = -41
Explanation:
The calculation shows that the number of families with both a radio and a TV is -41, which is not possible in this context. It suggests that there might be an error in the given information or its interpretation.
Therefore, the correct answer cannot be determined based on the given information. The option "None of these" is the appropriate choice in this case.
- Total number of families investigated = 1003
- Number of families with neither a radio nor a TV = 63
- Number of families with a radio = 794
- Number of families with a TV = 187
Calculating the number of families with both a radio and a TV:
To find the number of families that have both a radio and a TV, we need to subtract the number of families with neither a radio nor a TV from the total number of families.
Total number of families = Number of families with neither a radio nor a TV + Number of families with a radio + Number of families with a TV + Number of families with both a radio and a TV
1003 = 63 + 794 + 187 + Number of families with both a radio and a TV
Number of families with both a radio and a TV = 1003 - (63 + 794 + 187)
Number of families with both a radio and a TV = 1003 - 1044
Number of families with both a radio and a TV = -41
Explanation:
The calculation shows that the number of families with both a radio and a TV is -41, which is not possible in this context. It suggests that there might be an error in the given information or its interpretation.
Therefore, the correct answer cannot be determined based on the given information. The option "None of these" is the appropriate choice in this case.
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In a statistical investigation of 1003 families of Calcutta, it was found that 63 families has neither a radio nor a T.V, 794 families has a radio and 187 has T.V. The number of families in that group having both a radio and a T.V isa)36b)41c)32d)None of theseCorrect answer is option 'B'. Can you explain this answer?
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