Question

In a class, 60% of the students are girls and the rest are boys. There are 30 more girls than boys. If 68% of the students, including 30 boys, pass an examination, the percentage of the girls who do not pass is

• A. 10
• B. 20
• C. 30
• D. 25

Answer 1

The Correct Option is B

The problem requires us to find the percentage of girls who did not pass the examination in a class where 60% are girls, and the difference in number between girls and boys and passing information is provided.

1. Let the total number of students be N. 
2. Number of girls \( = 0.6N \).
3. Number of boys \( = 0.4N \).
4. We know there are 30 more girls than boys, so \( 0.6N = 0.4N + 30 \). Solving this gives:

\( 0.2N = 30 \). Thus, \( N = \frac{30}{0.2} = 150 \).

1. Substitute N to find the number of girls: \( 0.6 \times 150 = 90 \).
2. Number of boys: \( 0.4 \times 150 = 60 \).
3. 68% of the students pass the examination. The number of students who pass is:

\( \frac{68}{100} \times 150 = 102 \).

1. Given: 30 boys pass, so the number of girls who pass is:

\( 102 - 30 = 72 \).

1. Find the percentage of girls who do not pass: Number of girls who do not pass is \( 90 - 72 = 18 \).
2. Percentage of girls who do not pass is:

\( \frac{18}{90} \times 100 = 20\% \).

Thus, the percentage of the girls who do not pass is 20%.