The data given in the table shows the number of boys and girls interested in…
2025
The data given in the table shows the number of boys and girls interested in different sports in a school over 5 years. Find the ratio of number of boys interested in Tennis and Badminton to that of girls interested in Athletics over the 5 years?
years | Tennis | Athletics | Badminton | |||
|---|---|---|---|---|---|---|
Girls | Boys | Girls | Boys | Girls | Boys | |
2012 | 65 | 20 | 62 | 35 | 45 | 35 |
2014 | 72 | 22 | 45 | 32 | 42 | 32 |
2016 | 80 | 25 | 42 | 30 | 38 | 36 |
2018 | 62 | 30 | 46 | 23 | 34 | 28 |
2020 | 71 | 23 | 45 | 30 | 41 | 29 |
- A.
5 : 7
- B.
7 : 6
- C.
5 : 4
- D.
4 : 7
Attempted by 4 students.
Show answer & explanation
Correct answer: B
Concept: To find the ratio between a combined-category total (summed over several years) and another category's total over the same years, first read off the correct row-column intersection for every year, sum each category separately across all the years, and only then express the two grand totals as a ratio reduced to lowest terms.
Application:
From the table, read the Boys - Tennis value for each year: 20, 22, 25, 30, 23.
Add these five values: 20 + 22 + 25 + 30 + 23 = 120.
From the table, read the Boys - Badminton value for each year: 35, 32, 36, 28, 29.
Add these five values: 35 + 32 + 36 + 28 + 29 = 160.
Add the two boys' totals to get the combined total for Tennis and Badminton: 120 + 160 = 280.
From the table, read the Girls - Athletics value for each year: 62, 45, 42, 46, 45.
Add these five values to get the girls' Athletics total: 62 + 45 + 42 + 46 + 45 = 240.
Write the ratio of the two totals, 280 : 240, and divide both terms by their highest common factor, 40, to reduce it to 7 : 6.
Cross-check: Multiplying the reduced ratio 7 : 6 back by the common factor 40 gives 7 x 40 = 280 and 6 x 40 = 240, which matches the two totals computed above, confirming the simplification is correct.
Result: So the required ratio of the number of boys interested in Tennis and Badminton to the number of girls interested in Athletics, over the five years, is 7 : 6.