In 1995, the enrollment of two schools X and Y were 1,050 and 1,190 respectively. Find the ration of the enrollments of X and Y

Analyze the question: We are asked for the ratio of the enrollment of school X to that of school Y, in that order: X : Y = 1,050 : 1,190.

Concept: To simplify a ratio, divide both numbers by their highest common factor (HCF).

Solution:

1. Write the ratio: 1,050 : 1,190

2. Divide both by 10: 105 : 119

3. Find the common factor. Both are divisible by 7: • 105 ÷ 7 = 15 • 119 ÷ 7 = 17

4. Simplified ratio: 15 : 17

15 and 17 share no common factor other than 1, so this is the simplest form.

Check against the options:

• A. 50:11 – no
• B. 15:17 – matches
• C. 13:55 – no
• D. 12:11 – no

Tip: In ratio questions, first remove the trailing zeros (divide by 10, 100, etc.), then test small primes like 2, 3, 5, 7. Here, spotting that 105 = 7 × 15 and 119 = 7 × 17 quickly gives the answer. Also, always keep the order the question gives (X first, then Y).