Q.2 Out of a total of 130 students 60 are wearing hats to class, 51 are wearing
scarves and 30 are wearing both hats and scarves. Of the 54 students who
wearing sweaters, 26 are wearing hats, 21 are wearing scarves and 12 are
wearing both hats and scarves. Everyone wearing neither a hat nor a scarf is
wearing gloves.
(i) How many students are wearing gloves.
(ii) How many students not wearing a sweater are wearing hats but not scarve
Answers
Given : total of 130 students 60 are wearing hats to class, 51 are wearing
scarves and 30 are wearing both hats and scarves. Of the 54 students who
wearing sweaters, 26 are wearing hats, 21 are wearing scarves and 12 are
wearing both hats and scarves. Everyone wearing neither a hat nor a scarf is wearing gloves.
To Find : (i) How many students are wearing gloves.
(ii) How many students not wearing a sweater are wearing hats but not scarve
Solution:
Total Students = 130
Wearing Hat = 60
Wearing Scarves = 51
Wearing both Hat and Scarves = 30
Wearing Hats but not scarve = 60 - 30 = 30
Wearing Hat / Wearing Scarves or both = 60 + 51 - 30 = 81
wearing neither a hat nor a scarf = 130 - 81 = 49
=> wearing gloves = 49
Of the 54 students who wearing sweaters,
26 are wearing hats,
21 are wearing scarves
12 are wearing both hats and scarves.
Wearing sweater Wearing Hats but not scarve = 26 - 12 = 14
Wearing Hats but not scarve = 30
not wearing sweater Wearing Hats but not scarve = 30 - 14 = 16
not wearing sweater Wearing Hats but not scarve = 16
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