Question

# In a group of 950 persons, 750 can speak Hindi and 460 can speak English. Find: (i) how many can speak both Hindi and English: (ii) how many can speak Hindi only; (iii) how many can speak English only.

Open in App
Solution

## Let A & B denote the sets of the persons who like Hindi & English, respectively.$\mathrm{Given}:\phantom{\rule{0ex}{0ex}}n\left(A\right)=750\phantom{\rule{0ex}{0ex}}n\left(B\right)=460\phantom{\rule{0ex}{0ex}}n\left(A\cup B\right)=950\phantom{\rule{0ex}{0ex}}\left(\mathrm{i}\right)\mathrm{We}\mathrm{know}:\phantom{\rule{0ex}{0ex}}n\left(A\cup B\right)=n\left(A\right)+n\left(B\right)-n\left(A\cap B\right)\phantom{\rule{0ex}{0ex}}⇒950=750+460-n\left(A\cap B\right)\phantom{\rule{0ex}{0ex}}⇒n\left(A\cap B\right)=260\phantom{\rule{0ex}{0ex}}\mathrm{Thus},260\mathrm{persons}\mathrm{can}\mathrm{speak}\mathrm{both}\mathrm{Hindi}\mathrm{and}\mathrm{English}.\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\left(\mathrm{ii}\right)n\left(A-B\right)=n\left(A\right)-n\left(A\cap B\right)\phantom{\rule{0ex}{0ex}}n\left(A-B\right)=750-260=490\phantom{\rule{0ex}{0ex}}\mathrm{Thus},490\mathrm{persons}\mathrm{can}\mathrm{speak}\mathrm{only}\mathrm{Hindi}.\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\left(\mathrm{iii}\right)n\left(B-A\right)=n\left(B\right)-n\left(A\cap B\right)\phantom{\rule{0ex}{0ex}}⇒n\left(B-A\right)=460-260\phantom{\rule{0ex}{0ex}}=200\phantom{\rule{0ex}{0ex}}\mathrm{Thus},200\mathrm{persons}\mathrm{can}\mathrm{speak}\mathrm{only}\mathrm{English}.$

Suggest Corrections
0
Related Videos
Introduction to Decimal Fraction
MATHEMATICS
Watch in App
Explore more