In a survey 21 people know to read English, 26 know to read Tamil and 29 know to read Sanskrit. if 14 people can read both English and Tamil, 12 people can read both Sanskrit and English, 14 people know to read Tamil and Sanskrit, and 8 of them know to read all the three languages. Find, 1) how many know to read only Sanskrit. 2) if 50 were only surveyed, then how many did not know to speak any of the three languages? 3) how many know to speak English and Tamil but not Sanskrit. 4) how many know to speak either Tamil or Sanskrit. 5) how many know to speak English or Sanskrit but not Tamil?
Answers
Step-by-step explanation:
Total students=100
Only English =18
English but not hindi=23
English & sanskrit=8
English =26, sanskrit−48
Sanskrit & Hindi =8
No language =24
from above diagram we can see that no. of students studying Hindi=10+5+3
=18
No. of students studying English and Hindi=3.
E-English, H-Hindi, S-Sanskrit
We have,
Only English = a=18
English but not hindi = a+d=23
English & sanskrit = d+e=8
English = a+b+d+e=26
d+e+f+g=48
a+b+c+d+e+f+g=100−24=76
∴a=18,b=0,c=10,d=5,e=3,f=5 and g=35
n(H∩E)=b+e=3.
Solution:
Total students=100
Only English =18
English but not hindi=23
English & sanskrit=8
English =26, sanskrit−48
Sanskrit & Hindi =8
No language =24
from above diagram we can see that no. of students studying Hindi=10+5+3
=18
No. of students studying English and Hindi=3.
E-English, H-Hindi, S-Sanskrit
We have,
Only English = a=18
English but not hindi = a+d=23
English & sanskrit = d+e=8
English = a+b+d+e=26
d+e+f+g=48
a+b+c+d+e+f+g=100−24=76
∴a=18,b=0,c=10,d=5,e=3,f=5 and g=35
n(H∩E)=b+e=3.