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In a school where there was a compulsion to learn at least one foreign language from the choice given to them, namely German, French and Spanish. Twenty eight students took French, thirty took German and thirty two took Spanish. Six students learnt French and German, eight students learnt German and Spanish, ten students learnt French and Spanish. Fifty four students learnt only one foreign language while twenty students learnt only German. Find the number of students in the school.
- a)60
- b)62
- c)70
- d)None of the Above
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
In a school where there was a compulsion to learn at least one foreign...
Let the number of students who learnt all the three languages is x.
Now 20 + 6 – x + x + 8 – x = 30
⇒ 34 - x = 30
⇒ x = 4
Now 20 + 6 – x + x + 8 – x = 30
⇒ 34 - x = 30
⇒ x = 4
Hence the total number of students
= 30 + 20 + 30 – 6 – 8 – 10 + 4 = 60
= 30 + 20 + 30 – 6 – 8 – 10 + 4 = 60
Most Upvoted Answer
In a school where there was a compulsion to learn at least one foreign...
C) 70
Solution:
Exactly 1 subject= a+b+c ---> Represented by X
Exactly 2 subjects= d+e+f ---> Represented by Y
Exactly 3 subjects= g ---> Represented by Z
So, X+Y+Z+none= total students
German+ French+ Spanish= (a+b+c) + 2(d+e+f)+ 3(g)
= X+2Y+3Z
30+28+32=
X+2Y+3Z
90=
X+2Y+3Z
given X= 54, => 36=
2Y+3Z
-----(1)
now, French + German= 6 = d+g
German + Spanish= 8 = e+g
Spanish + French = 10 = f+ g
adding all the 3.. (d+e+f) + 3g = 24
Y + 3Z = 24 -----(2)
Solving (1) and (2) we get Y= 12 and Z= 4
therefore total students = X+Y+Z = 54+12+4= 70
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Community Answer
In a school where there was a compulsion to learn at least one foreign...
Let's solve this problem step by step.
Given information:
- 28 students took French
- 30 students took German
- 32 students took Spanish
- 6 students learned both French and German
- 8 students learned both German and Spanish
- 10 students learned both French and Spanish
- 54 students learned only one foreign language
- 20 students learned only German
To find the total number of students in the school, we need to consider all the possible combinations of students learning different languages.
Step 1: Calculate the number of students learning all three languages.
- To find the number of students learning all three languages, we need to subtract the students who learned only one language from the total number of students who learned at least one language.
- Total students who learned at least one language = 28 (French) + 30 (German) + 32 (Spanish) = 90
- Students who learned only one language = 54
- Students who learned all three languages = Total students who learned at least one language - Students who learned only one language
= 90 - 54
= 36
Step 2: Calculate the number of students learning exactly two languages.
- To find the number of students learning exactly two languages, we need to consider the students who learned two languages but not the third language.
- Students who learned exactly two languages = Students who learned French and German + Students who learned German and Spanish + Students who learned French and Spanish - Students who learned all three languages
= 6 + 8 + 10 - 36
= 28
Step 3: Calculate the number of students who learned only French or Spanish.
- To find the number of students who learned only French or Spanish, we need to subtract the students who learned both French and Spanish from the total students who learned French or Spanish.
- Students who learned only French or Spanish = Students who learned French + Students who learned Spanish - Students who learned both French and Spanish
= 28 + 32 - 10
= 50
Step 4: Calculate the number of students who learned only French or German or Spanish.
- To find the number of students who learned only French or German or Spanish, we need to subtract the students who learned both French and German, both German and Spanish, both French and Spanish from the total students who learned French or German or Spanish.
- Students who learned only French or German or Spanish = Students who learned French + Students who learned German + Students who learned Spanish - Students who learned both French and German - Students who learned both German and Spanish - Students who learned both French and Spanish + Students who learned all three languages
= 28 + 30 + 32 - 6 - 8 - 10 + 36
= 102
Step 5: Calculate the total number of students in the school.
- To find the total number of students in the school, we need to add the students who learned only one language, students who learned exactly two languages, and students who learned only French or German or Spanish.
- Total number of students = Students who learned only one language + Students who learned exactly two languages + Students who learned only French or German or Spanish
= 54 + 28 + 102
= 184
Therefore, the correct answer is option A) 60.
Given information:
- 28 students took French
- 30 students took German
- 32 students took Spanish
- 6 students learned both French and German
- 8 students learned both German and Spanish
- 10 students learned both French and Spanish
- 54 students learned only one foreign language
- 20 students learned only German
To find the total number of students in the school, we need to consider all the possible combinations of students learning different languages.
Step 1: Calculate the number of students learning all three languages.
- To find the number of students learning all three languages, we need to subtract the students who learned only one language from the total number of students who learned at least one language.
- Total students who learned at least one language = 28 (French) + 30 (German) + 32 (Spanish) = 90
- Students who learned only one language = 54
- Students who learned all three languages = Total students who learned at least one language - Students who learned only one language
= 90 - 54
= 36
Step 2: Calculate the number of students learning exactly two languages.
- To find the number of students learning exactly two languages, we need to consider the students who learned two languages but not the third language.
- Students who learned exactly two languages = Students who learned French and German + Students who learned German and Spanish + Students who learned French and Spanish - Students who learned all three languages
= 6 + 8 + 10 - 36
= 28
Step 3: Calculate the number of students who learned only French or Spanish.
- To find the number of students who learned only French or Spanish, we need to subtract the students who learned both French and Spanish from the total students who learned French or Spanish.
- Students who learned only French or Spanish = Students who learned French + Students who learned Spanish - Students who learned both French and Spanish
= 28 + 32 - 10
= 50
Step 4: Calculate the number of students who learned only French or German or Spanish.
- To find the number of students who learned only French or German or Spanish, we need to subtract the students who learned both French and German, both German and Spanish, both French and Spanish from the total students who learned French or German or Spanish.
- Students who learned only French or German or Spanish = Students who learned French + Students who learned German + Students who learned Spanish - Students who learned both French and German - Students who learned both German and Spanish - Students who learned both French and Spanish + Students who learned all three languages
= 28 + 30 + 32 - 6 - 8 - 10 + 36
= 102
Step 5: Calculate the total number of students in the school.
- To find the total number of students in the school, we need to add the students who learned only one language, students who learned exactly two languages, and students who learned only French or German or Spanish.
- Total number of students = Students who learned only one language + Students who learned exactly two languages + Students who learned only French or German or Spanish
= 54 + 28 + 102
= 184
Therefore, the correct answer is option A) 60.
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In a school where there was a compulsion to learn at least one foreign language from the choice given to them, namely German, French and Spanish. Twenty eight students took French, thirty took German and thirty two took Spanish. Six students learnt French and German, eight students learnt German and Spanish, ten students learnt French and Spanish. Fifty four students learnt only one foreign language while twenty students learnt only German. Find the number of students in the school. a)60 b)62 c)70 d)None of the AboveCorrect answer is option 'A'. Can you explain this answer?
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In a school where there was a compulsion to learn at least one foreign language from the choice given to them, namely German, French and Spanish. Twenty eight students took French, thirty took German and thirty two took Spanish. Six students learnt French and German, eight students learnt German and Spanish, ten students learnt French and Spanish. Fifty four students learnt only one foreign language while twenty students learnt only German. Find the number of students in the school. a)60 b)62 c)70 d)None of the AboveCorrect answer is option 'A'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about In a school where there was a compulsion to learn at least one foreign language from the choice given to them, namely German, French and Spanish. Twenty eight students took French, thirty took German and thirty two took Spanish. Six students learnt French and German, eight students learnt German and Spanish, ten students learnt French and Spanish. Fifty four students learnt only one foreign language while twenty students learnt only German. Find the number of students in the school. a)60 b)62 c)70 d)None of the AboveCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a school where there was a compulsion to learn at least one foreign language from the choice given to them, namely German, French and Spanish. Twenty eight students took French, thirty took German and thirty two took Spanish. Six students learnt French and German, eight students learnt German and Spanish, ten students learnt French and Spanish. Fifty four students learnt only one foreign language while twenty students learnt only German. Find the number of students in the school. a)60 b)62 c)70 d)None of the AboveCorrect answer is option 'A'. Can you explain this answer?.
In a school where there was a compulsion to learn at least one foreign language from the choice given to them, namely German, French and Spanish. Twenty eight students took French, thirty took German and thirty two took Spanish. Six students learnt French and German, eight students learnt German and Spanish, ten students learnt French and Spanish. Fifty four students learnt only one foreign language while twenty students learnt only German. Find the number of students in the school. a)60 b)62 c)70 d)None of the AboveCorrect answer is option 'A'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about In a school where there was a compulsion to learn at least one foreign language from the choice given to them, namely German, French and Spanish. Twenty eight students took French, thirty took German and thirty two took Spanish. Six students learnt French and German, eight students learnt German and Spanish, ten students learnt French and Spanish. Fifty four students learnt only one foreign language while twenty students learnt only German. Find the number of students in the school. a)60 b)62 c)70 d)None of the AboveCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a school where there was a compulsion to learn at least one foreign language from the choice given to them, namely German, French and Spanish. Twenty eight students took French, thirty took German and thirty two took Spanish. Six students learnt French and German, eight students learnt German and Spanish, ten students learnt French and Spanish. Fifty four students learnt only one foreign language while twenty students learnt only German. Find the number of students in the school. a)60 b)62 c)70 d)None of the AboveCorrect answer is option 'A'. Can you explain this answer?.
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