Question

How many students in the college know all the three languages?

• A. 108
• B. 132
• C. 169
• D. 137
• E. 142

Answer 1

The correct option is C 169

Number of students studying Dentistry $=\frac{1600\times 45}{100}=720$
Number of students studying Homoeopathy $=\frac{1600\times 55}{100}=880$
In Dentistry,
Number of boy students $=\frac{720\times 5}{8}=450$
Number girl students $=\frac{720\times 3}{8}=270$
In Boys,
Know only English $=\frac{450\times 16}{100}=72$
Know only Hindi $=\frac{450\times 10}{100}=45$
Know only Bengali $=\frac{450\times 4}{100}=18$
Know English and Hindi $=\frac{450\times 24}{100}=108$
Knows English and Bengali $=\frac{450\times 20}{100}=90$
Know Hindi and Bengali $=\frac{450\times 14}{100}=63$
Know All three languages
$=450-(72+45+18+108+90+63)=450-396=54$
In Girls,
Know only English $=\frac{270\times 20}{100}=54$
Know only Hindi $=\frac{270\times 10}{100}=27$
Know only Bengali $=\frac{10\times 270}{100}=27$
Know English and Hindi $=\frac{270\times 20}{100}=54$
Know English and Bengali $=\frac{270\times 20}{100}=54$
Know Hindi and Bengali $=\frac{270\times 10}{100}=27$
Know all three languages
$=270-(54+27+27+54+54+27)=270-243=27$
In Homoeopathy,
Number of boy students $=\frac{880\times 4}{11}=320$
Number of girl students $=\frac{880\times 7}{11}=560$
In Boys,
Know only English $=\frac{20\times 320}{100}=64$
Know only Hindi $=\frac{15\times 320}{100}=48$
Know only Bengali $=\frac{5\times 320}{100}=16$
Know English and Hindi $=\frac{15\times 320}{100}=48$
Know English and Bengali $=\frac{25\times 320}{100}=80$
Know Hindi and Bengali $=\frac{10\times 320}{100}=32$
Know All three languages
$=320-(64+48+16+48+80+32)=320-288=32$
In Girls,
Know only English $=\frac{15\times 560}{100}=84$
Know only Hindi $=\frac{15\times 560}{100}=84$
Know only Bengali $=\frac{5\times 560}{100}=28$
Know English and Hindi $=\frac{560\times 20}{100}=112$
Know English and Bengali $=\frac{560\times 20}{100}=112$
Know Hindi and Bengali $=\frac{560\times 15}{100}=84$
Know all three languages
$=560-(84+84+28+112+112+84)=560-504=56$
Total number of students knowing all the three languages $=54+27+32+56=169$