Question

In a club having 360 members, 40 play carrom, 96 play table tennis, 144 play badminton, and the remaining members play volley-ball. If no member plays two or more games, find the ratio of members who play carom to the number of those who play badminton.

Answer 1

Hint: First find the number of members who play volley-ball using the given data and then find the fraction of members who play carrom to the members who play badminton and simplify the fraction to get the desired result.

Complete step-by-step answer:
It is given in the problem that there are 360 members in the club, out of which 40 play carrom, 96 play table tennis, 144 play badminton, and remaining members play volley-ball. It is also given that no member of the club plays two or more games.
The goal of the problem is to find the ration of the members who play carrom to those members of the club who play badminton.
Total number of members$ = 360$
Members who play carrom$ = 40$
Members who play tennis$ = 96$
Members who play badminton$ = 144$
First, find the number of members who play volley-ball.
Members who play volley-ball$ = 360 - \left( {40 + 96 + 144} \right)$
Members who play volley-ball$ = 360 - 280$
Members who play volley-ball$ = 80$
So, there are 80 members in a club who play volley-ball.
Now, find the ration of the members who play carom to the number of those who play badminton.
Required ratio$ = \dfrac{{{\text{members who play carrom}}}}{{{\text{member who play badminton}}}}$
Substitute the values of the members:
Required ratio$ = \dfrac{{40}}{{144}}$
Required ratio$ = \dfrac{5}{{18}}$
So, the ratio of the member who plays carrom to the number of those who play badminton is $\dfrac{5}{{18}}$.

Note: The fraction of the members who play carrom to the members who play badminton in the lowest term is the ratio that is required in the problem, so express the fraction in the lowest term.