KCET 2021 Math Solved Paper

Let the total number of families be x.
Let A= number of families that own cell phones
n(A)=

65

100

×x
Let B= number of families that own scooter
n(B)=15000
and (A∩B)= number of families that own cell phones and scooter both
n(A∩B)=

15

100

×x
Here, n(A∪B)=x
n(A∪B)=n(A)+n(B)−n(A∩B)
x=

65x

100

+15000−

15x

100

⇒ 100x=65x+1500000−15x
⇒ 100x−50x=1500000
⇒ 50x=1500000
⇒ x=30000
Total number of families in the town is 30000.