Question

In a state with a population of `75 x 10^6`, 45% of them know Hindi, 22% know English, 18% know Sanskrit, 12% know. Hindi and English, 8% know English and Sanskrit, 10% know Hindi and Sanskrit and 5% known all the three languages What is the number of people who do not know any of the above three languages? What is the number of people who know only Hindi . What is the number of people who know only Sanskrit? What is the number of people who know only English? What is the number of people who know only one language? What is the number of people who know only two languages?
A. `11.25xx10^(5)`
B. `11.25xx10^(6)`
C. `12xx10^(5)`
D. `12.5xx10^(5)`

Answer 1

Correct Answer - C
Given, `P=75xx10^(6)`
45% population know Hindi
i.e., a+f+d+g=45% of P
`=(45)/(100)xx75xx10^(6)=33.75xx10^(6)" ....(1)"`
22% population know English
f+b+g+e=22% of P
`=(22)/(100)xx75xx10^(6)=16.50xx10^(6)" ....(2)"`
18% population know Sanskrit.

`d+g+e+c=18%" of P"`
`=18/100xx75xx10^(6)=13.5xx10^(6)" ....(3)"`
12% population knows Hindi and English
`f+g=12%" of P"=(12)/(100)xx75xx10^(6)=9xx10^(6)" ....(4)"`
8% population knows English and Sanskrit
`g+e=8% " of P"=(8)/(100)xx75xx10^(6)=6xx10^(6)" ....(5)"`
10% population Hindi and Sanskrit
`g+d=10% " of P"=(10)/(100)xx75xx10^(6)=7.5xx10^(6)" ....(6)"`
5% population knows all three languages
`g=5%"of P"=(5)/(100)xx75xx10^(6)=3.75xx10^(6)" ....(7)"`
From (6), (7) `3.75xx10^(6)+d=7.5xx10^(6)`
`impliesd=10^(6)(7.5-3.75)=3.75xx10^(6)`
From (5), (7) `3.75xx106+e=6xx10^(6)`
`impliese=10^(6)(6-3.75)=2.25xx106`
From(4), (7) implies `f+3.75xx106=9xx10^(6)`
`implies f=10^(6)(9-3.75)=5.25xx10^(6)`
From(2), `b=16.5xx10^(6)-(f+g+e)`
`=16.5xx10^(6)-(5.25xx10^(6)+3.75xx10^(6)+2.25xx10^(6))`
`=10^(6)[16.5-5.25-3.75-2.25]=5.25xx10^(6)`
From (3), `c=13.5xx10^(6)-(d+g+e)`
`=13.5xx10^(6)-9.75xx10^(6)=3.75xx10^(6)`
From (4), `a=33.75xx10^(6)-(f+g+d)`
`=33.75xx10^(6)-12.75xx10^(6)=21xx10^(6)`
`=d+e+f=3.75xx10^(6)+2.25xx10^(6)+5.25xx10^(6)`
`=11.25xx10^(6)`