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In a town of 400 people, 185 speak Tamil, 165 speak Punjabi, and 160 speak English. 40 people speak only English and Tamil. 20 people speak only Punjabi and Tamil. 10 people speak only English and Punjabi. How many people speak only one language?

In a town of 400 people, 185 speak Tamil, 165 speak Punjabi, and 160 speak English. 40 people speak only English and Tamil. 20 people speak only Punjabi and Tamil. 10 people speak only English and Punjabi. How many people speak only one language? Correct Answer 310

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No. of people who speak Tamil = 185

No. of people who speak English = 160

No. of people who speak Punjabi = 165

Now, 

No. of people who speak only English and Tamil is = 40

No. of people who speak only Punjabi and Tamil is = 20

No. of people who speak only English and Punjabi is = 10

Let No. of people who speak Punjabi, Tamil and English all is = x ;

So, only Tamil speaking is = 185 - 40 - 20 - x = 125 - x ;

Only English speaking is = 160 - 40 -10 - x = 110 - x ;

Only Punjabi speaking is = 165 - 20 - 10 - x = 135 - x ;

Now, (125 - x) + (110 - x) + (135 - x) + 20 + 40 + 10 + x  = 440 - 2x = 400 

So, x = 20 this is the value who speak all the three languages.

So, No. of people who read only one language is = (125 - 20) + (110 -20) + (135-20) = 105 + 90 + 115 = 310.

Hence there are 310 people who speak only one language.

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