Understanding Student Participation in Sports

The question asks us to find the ratio of the number of students who like to play cricket in Class B to the number of students who like to play football in Class C. We need to use the data provided in the table to determine these numbers.

Analyzing the Provided Data Table

The table gives us the total number of students in each class and the percentage of students who like different sports within each class. Let's focus on the relevant information for Class B and Class C.

Calculating Students Liking Cricket in Class B

From the table, the total number of students in Class B is 280. The percentage of students in Class B who like cricket is 50%. To find the number of students who like cricket in Class B, we calculate 50% of 280.

Number of students liking Cricket in Class B $$ = \frac{50}{100} \times 280 $$

$$ = 0.50 \times 280 $$

$$ = 140 $$

So, 140 students in Class B like to play cricket.

Calculating Students Liking Football in Class C

From the table, the total number of students in Class C is 320. The percentage of students in Class C who like football is 45%. To find the number of students who like football in Class C, we calculate 45% of 320.

Number of students liking Football in Class C $$ = \frac{45}{100} \times 320 $$

$$ = 0.45 \times 320 $$

$$ = 144 $$

So, 144 students in Class C like to play football.

Determining the Ratio of Students Liking Cricket in Class B to Football in Class C

We need to find the ratio of the number of students who like cricket in Class B to the number of students who like football in Class C. This ratio is:

Ratio $$ = (\text{Number of students liking Cricket in Class B}) : (\text{Number of students liking Football in Class C}) $$

Ratio $$ = 140 : 144 $$

Simplifying the Ratio

To simplify the ratio 140 : 144, we need to find the greatest common divisor (GCD) of 140 and 144 and divide both numbers by it.

• Factors of 140: 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140
• Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144

The greatest common divisor (GCD) of 140 and 144 is 4.

Divide both parts of the ratio by 4:

$$ \frac{140}{4} : \frac{144}{4} $$

$$ 35 : 36 $$

The simplified ratio of students liking cricket in Class B to students liking football in Class C is 35 : 36.

Conclusion

The ratio of the number of students who like to play cricket in Class B to that of the number of students who like to play Football in Class C is 35 : 36.

Revision Table: Student Sports Participation Ratio

Additional Information: Calculating Percentages and Ratios

Calculating the number of students from a given percentage and total involves multiplying the total number by the percentage expressed as a decimal or fraction. For example, to find P% of a number N, you calculate $$(P/100) \times N$$.

A ratio compares two quantities. A ratio a : b can be simplified by dividing both 'a' and 'b' by their greatest common divisor (GCD). This process finds the simplest form of the ratio while maintaining the relationship between the two quantities. Ratios are often used to compare parts of a whole or compare different quantities relative to each other, as seen in comparing student participation in different sports across classes. Understanding how to calculate percentages and simplify ratios is fundamental for interpreting data presented in tables like the one showing class-wise student participation in sports.