400 students took a mock exam in Delhi. 60% of the boys and 80% of the girls cleared the cut off in the examination. If the total percentage of students qualifying is 65%, how many girls appeared in the examination?a)100b)120c)150d)300Correct answer is option 'A'. Can you explain this answer?

Question

Answer

The ratio of boys and girls appearing for the exam can be seen to be 3:1 using the following alligation figure.

This means that out of 400 students, there must have been 100 girls who appeared in the exam.

Answer

Given data:
- Total number of students who took the mock exam = 400
- Percentage of students who cleared the cut off = 65%
- Percentage of boys who cleared the cut off = 60%
- Percentage of girls who cleared the cut off = 80%

To find: Number of girls who appeared in the examination

Solution:
Let the number of boys be 'b' and the number of girls be 'g' who appeared for the examination.

Total number of students who cleared the cut off = 65% of 400 = (65/100)*400 = 260

Number of boys who cleared the cut off = 60% of b = (60/100)*b

Number of girls who cleared the cut off = 80% of g = (80/100)*g

Total number of students who cleared the cut off = Number of boys who cleared the cut off + Number of girls who cleared the cut off

(60/100)*b + (80/100)*g = 260

Simplifying the above equation, we get:

6b + 8g = 2600 (dividing by 10)

3b + 4g = 1300 (dividing by 2)

Now, we need to find the value of 'g' (number of girls). We can use the method of options to check which option satisfies the above equation.

a) If g = 100, then 3b + 4g = 3b + 400 = 1300, which gives b = 300.
So, the total number of students who cleared the cut off = (60/100)*300 + (80/100)*100 = 180 + 80 = 260 (which matches the given data).
Hence, option A is correct.

b) If g = 120, then 3b + 4g = 3b + 480 = 1300, which gives b = 273.33 (not possible as b should be a whole number).

c) If g = 150, then 3b + 4g = 3b + 600 = 1300, which gives b = 233.33 (not possible as b should be a whole number).

d) If g = 300, then 3b + 4g = 3b + 1200 = 1300, which gives b = 33.33 (not possible as b should be a whole number).

Therefore, the correct answer is option A, i.e., 100 girls appeared in the examination.

Similar Quant Doubts

In an examination of CAT out of 560 students from an institution, 80% of the girls and 70% of the boys scored more than 95%ile. How many boys appeared in the examination if the total percentage of students who scored more than 95 percentile is 75%.

In an examination, 50% of the students passed in Science and 75% passed in Social, while 20% students failed in both the subjects. If 270 students passed in both subjects, find the total number of students who appeared in the exam?

In an examination, 80% students passed in philosophy and 70% students passed in maths. At the same time 15% failed in both the subjects. If390 students passed in both the subjects, how many students appeared in the examination?

Out of the three annual examinations, each with a total of 500 marks, a student secured average marks of 45% and 55% in the first and second annual examinations. To have an overall average of 60%, how many marks does the student need to secure in the third annual examination ?

Top Courses for Quant

Suggested Free Tests

Related Content

Quant Courses

Related Exams

Related Question Answers

Related Searches

Company