Question

In a survey of 125 students of class 10 in a school, 65 preferred to visit lumbini, 75 preferred to visit Pokhara and 25 preferred both places in their annual excursion. (I) show above information in a venn-diagram (ii) find number of students who liked neither of two places (iii) find the number of students who liked only Lumbini

Answer 1

i)10students ii) 40students

Explanation:

n(u)=125

n(lumbini)=65

n(pokhara)=75

n(lumbini n pokhara)=25

For lumbini only

let represent x for it

therefore x+25=65

x=65-25

=40students

For Pokhara only

25+y=75

y=75-25

= 50

For students who neither liked the two places

40+25+50+z=125

115+z=125

z=125-115

=10

Answer 2

Explanation:

(ii) Number of students who liked neither of the two places:

To find the number of students who liked neither Lumbini nor Pokhara, we need to subtract the total number of students who preferred either place or both from the total number of students (125):

Total students who liked Lumbini or Pokhara or both = 65 + 75 - 25 = 115

Number of students who liked neither = Total students - Total students who liked Lumbini or Pokhara or both = 125 - 115 = 10

Therefore, there are 10 students who liked neither of the two places.

(iii) Number of students who liked only Lumbini:

To find the number of students who liked only Lumbini, we subtract the number of students who liked both places from the total number of students who preferred Lumbini:

Number of students who liked only Lumbini = Total students who liked Lumbini - Students who liked both places = 65 - 25 = 40

Therefore, there are 40 students who liked only Lumbini.