Question

A certain club has 100 members, out of which 25 play tennis, 28 play badminton, 12 play chess and the rest do not play any games. Find the ratio of number of members who play badminton to the number of those who play chess.

Answer 1

Hint: We solve this question by using the given data. We are given the number of people who play tennis, badminton and chess in a club. We are required to find the ratio of the number of people who play badminton to the number of people who play chess. This is done simply by dividing the two numbers and reducing to a simple form and representing it in the form of a ratio.

Complete step by step answer:
In order to solve this question, let us first write down the given data. This is required for us to simplify our data so that we can find the solution easily.
The number of members in the club is given by,
$\Rightarrow \text{No}\text{. of members in the club=100}$
The number of members who play tennis is given by,
$\Rightarrow \text{No}\text{. of members who play tennis=25}$
The number of members who play badminton is given by,
$\Rightarrow \text{No}\text{. of members who play badminton=28}$
The number of members who play chess is given by,
$\Rightarrow \text{No}\text{. of members who play chess=12}$
The number of members who do not play any game can be found by subtracting the total number of members in the club by the sum of the members who play tennis, badminton and chess.
$\Rightarrow \text{No}\text{. of members who do not play any game=}100-\left( 25+28+12 \right)$
Adding the number of terms and subtracting from 100,
$\Rightarrow \text{No}\text{. of members who do not play any game=}100-65=35$
Now, we are required to find the ratio of the number of members who play badminton to the number of people who play chess. This given by simply dividing the two.
$\Rightarrow \dfrac{\text{No}\text{. of members who play badminton}}{\text{No}\text{. of members who play chess}}\text{=}\dfrac{28}{12}$
This can be simplified further since the numerator and denominator have a common factor of 4. Taking this out from the numerator and denominator,
$\Rightarrow \dfrac{\text{No}\text{. of members who play badminton}}{\text{No}\text{. of members who play chess}}\text{=}\dfrac{7\times 4}{3\times 4}$
Cancelling the 4 from the numerator and denominator,
$\Rightarrow \dfrac{\text{No}\text{. of members who play badminton}}{\text{No}\text{. of members who play chess}}\text{=}\dfrac{7}{3}$
This can be represented as a ratio given by $7:3.$ Hence, the ratio of number of members who play badminton to the number of those who play chess is $7:3.$

Note: We need to know the concept of ratio and proportion to solve this question. It is important to note that sometimes it becomes necessary to represent the answer in its simplest form which can be done by taking out a common factor for the numerator and denominator and cancelling it out. A ratio is generally represented with a colon in between as shown above and is read as 7 is to 3.