The given bar-graph shows the favourite sports of 540 students of a school.…
2026
The given bar-graph shows the favourite sports of 540 students of a school.
Study the graph and answer the question that follows.
Find the ratio between the number of students who like Cricket to the number of students who like Badminton.
Answer: B. 12 : 5 — Concept: A ratio compares two quantities by division. The ratio of a to b is written a : b, and it is brought to its lowest terms by dividing both parts by…
- A.
8 : 5
- B.
12 : 5
- C.
10 : 3
- D.
7 : 3
Attempted by 78 students.
Show answer & explanation
Correct answer: B
Concept: A ratio compares two quantities by division. The ratio of a to b is written a : b, and it is brought to its lowest terms by dividing both parts by their HCF (highest common factor). Reducing never changes what the ratio means, because both parts are scaled down by the same factor. In a bar graph the height of each bar is the value of that category, so a ratio between two categories depends just on those two bars — the overall total is not needed to form it.
Reading the graph, the five bars give these counts:
Sport | Number of students |
|---|---|
Cricket | 180 |
Football | 100 |
Tennis | 80 |
Badminton | 75 |
Swimming | 105 |
Applying the concept to Cricket and Badminton:
The Cricket bar stands at 180, so 180 students like Cricket.
The Badminton bar stands at 75, so 75 students like Badminton.
The question asks for Cricket to Badminton, in that order, so write the comparison as 180 : 75.
Divide both parts by 5: 180 ÷ 5 is 36, and 75 ÷ 5 is 15, which gives 36 : 15.
Divide both parts by 3: 36 ÷ 3 is 12, and 15 ÷ 3 is 5, which gives 12 : 5.
No whole number greater than 1 divides both 12 and 5, so 12 : 5 is the ratio in its lowest terms.
Cross-check: scaling 12 : 5 back up by 15 returns 12 × 15 = 180 and 5 × 15 = 75, the two bar values we started from. As an independent decimal check, 180 ÷ 75 = 2.4 and 12 ÷ 5 = 2.4, and the two agree. The bar readings themselves are confirmed by the total given in the question: 180 + 100 + 80 + 75 + 105 = 540. Mind the order of the comparison: turning it around to Badminton against Cricket would give 75 : 180 = 5 : 12, which is a different ratio.