Question:
In an examination of 12600 students, the ratio of the number of boys to the number of girls is 3:4. The ratio of the number of students who passed the exam to those who failed the exam is in the ratio of 11:3. Among the girls, the ratio of the number of students who passed to those who failed the exam is in ratio 11:4. Find the difference between the number of boys who passed and failed the exam.
In an examination of 12600 students, the ratio of the number of boys to the number of girls is 3:4. The ratio of the number of students who passed the exam to those who failed the exam is in the ratio of 11:3. Among the girls, the ratio of the number of students who passed to those who failed the exam is in ratio 11:4. Find the difference between the number of boys who passed and failed the exam.
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When dealing with ratio-based problems, break down the information into smaller parts, calculate individual groups, and then find the required difference.
Updated On: Nov 4, 2025
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Solution and Explanation
Step 1: Understanding the ratios.
We are given the ratio of boys to girls and the ratio of passed to failed students among boys and girls. First, calculate the total number of boys and girls. The total number of boys = \( \frac{3}{7} \times 12600 = 5400 \) and the total number of girls = \( \frac{4}{7} \times 12600 = 7200 \).
Step 2: Breakdown of passed and failed students.
- The total number of students who passed the exam = \( \frac{11}{14} \times 12600 = 9900 \).
- The total number of students who failed the exam = \( \frac{3}{14} \times 12600 = 2700 \).
Among girls, the ratio of passed to failed students is 11:4, so the number of girls who passed = \( \frac{11}{15} \times 7200 = 5280 \), and the number of girls who failed = \( \frac{4}{15} \times 7200 = 1920 \).
Step 3: Finding the number of boys who passed and failed.
- Number of boys who passed = Total boys - Girls who passed = \( 9900 - 5280 = 4620 \).
- Number of boys who failed = Total boys - Girls who failed = \( 5400 - 1920 = 3480 \).
Step 4: Conclusion.
The difference between the number of boys who passed and failed is \( 4620 - 3480 = 1000 \). Hence, the correct answer is (C) 1000.
We are given the ratio of boys to girls and the ratio of passed to failed students among boys and girls. First, calculate the total number of boys and girls. The total number of boys = \( \frac{3}{7} \times 12600 = 5400 \) and the total number of girls = \( \frac{4}{7} \times 12600 = 7200 \).
Step 2: Breakdown of passed and failed students.
- The total number of students who passed the exam = \( \frac{11}{14} \times 12600 = 9900 \).
- The total number of students who failed the exam = \( \frac{3}{14} \times 12600 = 2700 \).
Among girls, the ratio of passed to failed students is 11:4, so the number of girls who passed = \( \frac{11}{15} \times 7200 = 5280 \), and the number of girls who failed = \( \frac{4}{15} \times 7200 = 1920 \).
Step 3: Finding the number of boys who passed and failed.
- Number of boys who passed = Total boys - Girls who passed = \( 9900 - 5280 = 4620 \).
- Number of boys who failed = Total boys - Girls who failed = \( 5400 - 1920 = 3480 \).
Step 4: Conclusion.
The difference between the number of boys who passed and failed is \( 4620 - 3480 = 1000 \). Hence, the correct answer is (C) 1000.
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