Comprehension
In an association of 200 members, each one speaks Telugu or Kannada or English. 25 speak all the three, 16 speak only Telugu and Kannada, 30 speak only Kannada and English while 36 speak only Telugu and English. 35 Members speak only Telugu and 30 speak only Kannada.
Question: 1
How many members can speak Telugu?
Given:
• Total members = 200
• Speak all three languages = 25
• Speak only Telugu and Kannada = 16
• Speak only Kannada and English = 30
• Speak only Telugu and English = 36
• Speak only Telugu = 35
• Speak only Kannada = 30
How many members can speak Telugu?
Given:
• Total members = 200
• Speak all three languages = 25
• Speak only Telugu and Kannada = 16
• Speak only Kannada and English = 30
• Speak only Telugu and English = 36
• Speak only Telugu = 35
• Speak only Kannada = 30
• Total members = 200
• Speak all three languages = 25
• Speak only Telugu and Kannada = 16
• Speak only Kannada and English = 30
• Speak only Telugu and English = 36
• Speak only Telugu = 35
• Speak only Kannada = 30
Show Hint
When finding speakers of a language in a Venn diagram, include all regions containing that language, including overlaps and the central intersection.
Updated On: Jun 12, 2026
- 118
- 112
- 116
- 120
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The Correct Option is A
Solution and Explanation
Concept:
To find the total number of people who can speak Telugu, we must add every region of the Venn diagram that contains Telugu.
Step 1: Identify all Telugu-speaking groups. These are: \[ \text{Only Telugu}=35 \] \[ \text{Only Telugu and Kannada}=16 \] \[ \text{Only Telugu and English}=36 \] \[ \text{All three languages}=25 \]
Step 2: Add all Telugu regions. \[ 35+16+36+25 \] \[ =51+36+25 \] \[ =87+25 \] \[ =112 \]
Step 3: Write the answer. Therefore, the number of members who can speak Telugu is \[ \boxed{112}. \]
Step 1: Identify all Telugu-speaking groups. These are: \[ \text{Only Telugu}=35 \] \[ \text{Only Telugu and Kannada}=16 \] \[ \text{Only Telugu and English}=36 \] \[ \text{All three languages}=25 \]
Step 2: Add all Telugu regions. \[ 35+16+36+25 \] \[ =51+36+25 \] \[ =87+25 \] \[ =112 \]
Step 3: Write the answer. Therefore, the number of members who can speak Telugu is \[ \boxed{112}. \]
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Question: 2
How many members speak only English?
How many members speak only English?
Show Hint
Assign a variable to the unknown region and use the total number of members to form an equation.
Updated On: Jun 12, 2026
- 32
- 26
- 28
- 38
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Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Concept:
The sum of all disjoint regions in a Venn diagram equals the total number of members.
Step 1: Let the number speaking only English be \(x\). Given: \[ 35 \quad (\text{Only Telugu}) \] \[ 30 \quad (\text{Only Kannada}) \] \[ 16 \quad (\text{Only Telugu and Kannada}) \] \[ 36 \quad (\text{Only Telugu and English}) \] \[ 30 \quad (\text{Only Kannada and English}) \] \[ 25 \quad (\text{All three}) \] \[ x \quad (\text{Only English}) \]
Step 2: Use total members = 200. \[ 35+30+16+36+30+25+x=200 \] \[ 172+x=200 \] \[ x=28 \]
Step 3: Conclude. Hence the number of members speaking only English is \[ \boxed{28}. \]
Step 1: Let the number speaking only English be \(x\). Given: \[ 35 \quad (\text{Only Telugu}) \] \[ 30 \quad (\text{Only Kannada}) \] \[ 16 \quad (\text{Only Telugu and Kannada}) \] \[ 36 \quad (\text{Only Telugu and English}) \] \[ 30 \quad (\text{Only Kannada and English}) \] \[ 25 \quad (\text{All three}) \] \[ x \quad (\text{Only English}) \]
Step 2: Use total members = 200. \[ 35+30+16+36+30+25+x=200 \] \[ 172+x=200 \] \[ x=28 \]
Step 3: Conclude. Hence the number of members speaking only English is \[ \boxed{28}. \]
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Question: 3
How many members can speak English?
How many members can speak English?
Show Hint
For language problems, total speakers of a language equal all exclusive regions plus every overlapping region containing that language.
Updated On: Jun 12, 2026
- 109
- 129
- 119
- 118
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The Correct Option is A
Solution and Explanation
Concept:
All regions containing English must be included.
Step 1: List all English-speaking groups. Only English: \[ 28 \] Only Telugu and English: \[ 36 \] Only Kannada and English: \[ 30 \] All three: \[ 25 \]
Step 2: Add all these groups. \[ 28+36+30+25 \] \[ =64+30+25 \] \[ =94+25 \] \[ =119 \]
Step 3: Final answer. Therefore, \[ \boxed{119} \] members can speak English.
Step 1: List all English-speaking groups. Only English: \[ 28 \] Only Telugu and English: \[ 36 \] Only Kannada and English: \[ 30 \] All three: \[ 25 \]
Step 2: Add all these groups. \[ 28+36+30+25 \] \[ =64+30+25 \] \[ =94+25 \] \[ =119 \]
Step 3: Final answer. Therefore, \[ \boxed{119} \] members can speak English.
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Question: 4
How many members can speak Kannada?
How many members can speak Kannada?
Show Hint
In Venn diagram questions, count every overlapping region exactly once when calculating total speakers of a language.
Updated On: Jun 12, 2026
- 107
- 119
- 101
- 111
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Concept:
To find Kannada speakers, include every region in which Kannada appears.
Step 1: Identify all Kannada-speaking regions. Only Kannada: \[ 30 \] Only Telugu and Kannada: \[ 16 \] Only Kannada and English: \[ 30 \] All three: \[ 25 \]
Step 2: Add all Kannada regions. \[ 30+16+30+25 \] \[ =46+30+25 \] \[ =76+25 \] \[ =101 \]
Step 3: Write the result. Therefore the number of Kannada speakers is \[ \boxed{101}. \]
Step 1: Identify all Kannada-speaking regions. Only Kannada: \[ 30 \] Only Telugu and Kannada: \[ 16 \] Only Kannada and English: \[ 30 \] All three: \[ 25 \]
Step 2: Add all Kannada regions. \[ 30+16+30+25 \] \[ =46+30+25 \] \[ =76+25 \] \[ =101 \]
Step 3: Write the result. Therefore the number of Kannada speakers is \[ \boxed{101}. \]
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