Question

A school has 2000 students, of which 40% of the students are in higher secondary. Out of the students in higher secondary 28% are girls of which 50% of them passed in an examination. How many boys from higher secondary have passed the examination?
Statement 1: The ratio between number of girls passed and number of boys passed in the school is 3:7
Statement 2: The overall pass percentage in the higher secondary is 40%

• A. Statement (1) alone is sufficient to answer the question
• B. Statement (2) alone is sufficient to answer the question
• C. Both the statements together are needed to answer the question
• D. Either statement (1) alone or statement (2) alone is sufficient to answer the question
• E. Neither statement (1) nor statement (2) suffices to answer the question

Answer 1

The Correct Option is B

The problem involves calculating the number of boys from higher secondary who have passed the examination based on the provided statements. We need to analyze each statement to determine if it provides sufficient data for solving the problem. 

1. First, let's determine the number of students in higher secondary:
   • Total students = 2000
   • Percentage of students in higher secondary = 40%
   • Number of students in higher secondary = \(2000 \times 0.40 = 800\)
2. Next, we calculate the number of girls in higher secondary:
   • Percentage of girls in higher secondary = 28%
   • Number of girls in higher secondary = \(800 \times 0.28 = 224\)
3. From the given data, among the girls who passed, 50% passed the examination:
   • Number of girls passed = \(224 \times 0.50 = 112\)
4. Now, let's evaluate each statement.
5. Statement 1 states the ratio between the number of girls passed to boys passed in the school is 3:7:
   • Using this, the number of boys passed in the ratio form would be \(\frac{7}{3} \times 112 \approx 261.33\)
   • Since boys passed must be a whole number, relying solely on this statement ends up being inconclusive due to the non-integral figure.
6. Statement 2 states that the overall pass percentage in higher secondary is 40%:
   • Total students in higher secondary (passed) = \(800 \times 0.40 = 320\)
   • Boys passed = Total passed - Girls passed = \(320 - 112 = 208\)
   • This statement directly results in the number of boys passing, solving the problem.

Hence, Statement (2) alone is sufficient to determine the number of boys from higher secondary who have passed the examination. Therefore, the correct option is:

 

Statement (2) alone is sufficient to answer the question