Question

A club has 180 students and all the students play at least one sport among lawn tennis, cricket and football. Total number of 85 students just play one sport, whereas the number of students playing both lawn tennis and cricket is five times the number of students playing all three sports. The number of students playing all three sports is half the number of students playing both cricket and football The average number of students playing all three sports and the number of students playing cricket and football is equal to the number of students playing both football and lawn tennis. The number of students playing both lawn tennis and football but not cricket is 15. The number of students who play cricket is 134 and the difference between the number of students who play only lawn tennis and only football is 3. How many students play cricket and one of the other sports but not all three?
Options
A 70
B 80
C 50
D 134

Answer 1

Answer:

In △ABC AB=AC

⇒∠B=∠C (Angles opposite to equal sides are equal)

Now using angle sum property

∠A+∠B+∠C=180

∘

⇒80

∘

+∠C+∠C=180

∘

⇒2∠C=180

∘

−80

∘

⇒∠C=

2

100

∘

=50

∘

now ∠C+∠x=180

∘

(Angles made on straight line (AC) are supplementary)

⇒50

∘

+∠x=180

∘

⇒∠x=180

∘

−50

∘

=130

∘

yo yo yo

@ARSH