Q.1 The ratio of boys to girls in a class is 7 to 3.
Among the options below, an acceptable value for the total number of
students in the class is:
(A) 21
(B) 37
(C) 50
(D) 73
Correct Answer: (C) 50
Option (C) 50 is the only acceptable total. Here’s why: Divide 50 by 10 parts = 5 per part. Boys = \(7 \times 5 = 35\), girls = \(3 \times 5 = 15\). Both are whole numbers, fitting the 7:3 ratio perfectly (35:15 simplifies to 7:3).
Explanation of All Options
Let’s test each option by checking if it divides evenly into 10 parts, yielding integers for boys and girls.
- Option (A) 21: 21 ÷ 10 = 2.1 parts. Boys = \(7 \times 2.1 = 14.7\), girls = \(3 \times 2.1 = 6.3\). Fractions aren’t possible for students, so invalid.
- Option (B) 37: 37 ÷ 10 = 3.7 parts. Boys = \(7 \times 3.7 = 25.9\), girls = \(3 \times 3.7 = 11.1\). Not whole numbers—invalid.
- Option (C) 50: As above, boys = 35, girls = 15. Perfect fit—valid.
- Option (D) 73: 73 ÷ 10 = 7.3 parts. Boys = \(7 \times 7.3 = 51.1\), girls = \(3 \times 7.3 = 21.9\). Fractions again—invalid.
| Option | Total Students | Parts per Student | Boys | Girls | Valid? |
|---|---|---|---|---|---|
| (A) | 21 | 2.1 | 14.7 | 6.3 | No |
| (B) | 37 | 3.7 | 25.9 | 11.1 | No |
| (C) | 50 | 5 | 35 | 15 | Yes |
| (D) | 73 | 7.3 | 51.1 | 21.9 | No |
Quick Tip for Ratio Problems
To solve boys to girls ratio 7:3 total students questions, find the least common multiple (LCM) of the ratio parts (10 here). Valid totals are multiples of 10: 10, 20, 30, 40, 50, etc. Among the options, only 50 qualifies.
Mastering these helps in exams like competitive tests or school math. Practice with similar ratios for speed.
