In a city school during the admission to class XI, 18 students took English, 23 took Hindi and 24 students took Sanskrit. Of these, 13 took both Hindi and Sanskrit, 12 took both English and Hindi and 11 took both English and Sanskrit. Due to the request made by the students, the school authorities decided that 6 students will be offered all the three languages. Kindly also provide the Venn digram
Based on the above information answer the following:
(i) The total number of students who took admission in class XI, is
(a) 35
(b) 30
(c) 33
(d) 45
(ii) How many students took Sanskrit but not Hindi?
(a) 6
(b) 19
(c) 11
(d) 9
(iii) How many students took exactly one of the three subjects?
(a) 25
(b) 11
(c) 20
(d) 21
(iv) How many students took exactly two of the three subjects?
(a) 11
(b) 21
(c) 8
(d) 18
(v) How many students took Hindi but not Sanskrit?
(a) 9
(b) 10
(c) 19
(d) 13
Answers
Answer:
In a city school during the admission to class XI, 18 students took English, 23 students took
Hindi and 24 students took Sanskrit.
Of these, 13 took both Hindi and Sanskrit, 12 took both English and Hindi and 11 took both
English and Sanskrit.
Due to the request made by some students, the school authorities decided that 6 students will
be offered all the three languages.
1. 35
2. 11
3. 11
4. 18
5. 9
Concept:
A Venn diagram represents the relation between data or set.
Given:
Number of students who took English = 18
Number of students who took Sanskrit = 23
Number of students who took Hindi = 24
Number of students who took both Hindi and Sanskrit = 13
Number of students who took both English and Hindi = 12
Number of students who took both English and Sanskrit = 11
Number of students who took all the three = 6
Find:
We are asked to seek out;
A. The total number of students who took admission in class XI.
B. Number of students took Sanskrit but not Hindi.
C. Number of students took exactly one of the three subjects.
D. Number of students took exactly two of the three subjects.
E. Number of students took Hindi but not Sanskrit.
Solution:
According to the given data,
A. The total number of students who took admission in class XI;
= 18 + 23 + 24 - (13 + 12 + 11) + 6
= 65 - 36 + 6
= 35
So, The total number of students who took admission in class XI is 35.
B. Number of students who took Sanskrit but not Hindi;
= 35 - 6 - 23
= 6
So, the number of students who took Sanskrit but not Hindi is 6.
C. Number of students took exactly one of the three subjects;
= 18 + 23 + 24 – 2 x 11 – 2 x 12 – 2 x 13 + 3 x 6
= 65 – 22 – 24 – 26 + 18
= 83 – 72
= 11
So, the number of students who took exactly one of the three subjects is 11.
D. Number of students took exactly two of the three subjects;
= 35 - 6
= 29
So, the number of students who took exactly two of the three subjects is
E. Number of students took Hindi but not Sanskrit;
= 23 - 13
= 10
So, the number of students who took Hindi but not Sanskrit is 10.
Hence we can say that , the total number of students who took admission in class XI is 35.
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