As per recent data, six private colleges - A, B, C, D, E, and F in Delhi had a total of 15000 students taking admission in undergraduate (UG) courses and 10000 students taking admission in postgraduate (PG) courses.In college A, the ratio of UG to PG admissions is 21 : 10. 16% of total students taking admission in UG courses went to college B. 19% of total students taking admission in UG courses went to college C which is 300 more than the student's taking admission in UG courses in college D. Equal number of students take admission in PG courses in college B and D. The ratio of PG admission in college A and F is 1 : 2 respectively. In college E, 26% of total PG admissions take admission which is 600 more than PG admissions in college F. Total number of admissions in college E is equal to 5900 and the same for college B is 4200.Q 115. How many PG admissions were there in college C?a) 800b) 1000c) 1200d) 1250
Question
As per recent data, six private colleges - A, B, C, D, E, and F in Delhi had a total of 15000 students taking admission in undergraduate (UG) courses and 10000 students taking admission in postgraduate (PG) courses.In college A, the ratio of UG to PG admissions is 21 : 10. 16% of total students taking admission in UG courses went to college B. 19% of total students taking admission in UG courses went to college C which is 300 more than the student's taking admission in UG courses in college D. Equal number of students take admission in PG courses in college B and D. The ratio of PG admission in college A and F is 1 : 2 respectively. In college E, 26% of total PG admissions take admission which is 600 more than PG admissions in college F. Total number of admissions in college E is equal to 5900 and the same for college B is 4200.Q 115. How many PG admissions were there in college C?a) 800b) 1000c) 1200d) 1250
Solution
To solve this problem, we need to first find out the number of UG and PG admissions in each college based on the given information.
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College A: The ratio of UG to PG admissions is 21:10. Let's assume the total number of students in college A is x. So, 21x/31 is the number of UG admissions and 10x/31 is the number of PG admissions.
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College B: 16% of total UG admissions, which is 0.16*15000 = 2400 students. The number of PG admissions is not given directly, but it's mentioned that it's equal to the number of PG admissions in college D.
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College C: 19% of total UG admissions, which is 0.19*15000 = 2850 students. The number of PG admissions is not given.
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College D: The number of UG admissions in college D is 300 less than in college C, which is 2850 - 300 = 2550 students. The number of PG admissions is equal to the number of PG admissions in college B.
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College E: The total number of admissions is 5900. The number of PG admissions is 26% of total PG admissions, which is 0.26*10000 = 2600 students. So, the number of UG admissions is 5900 - 2600 = 3300 students.
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College F: The number of PG admissions is 600 less than in college E, which is 2600 - 600 = 2000 students. The number of UG admissions is not given, but it's mentioned that the ratio of PG admissions in college A and F is 1:2. So, the number of PG admissions in college A is 2000/2 = 1000 students.
Now, we can find out the total number of PG admissions in all colleges, which is 10000. Subtracting the known PG admissions from this total, we get the number of PG admissions in college C.
10000 - (1000 (A) + 2400 (B) + 2600 (E) + 2000 (F)) = 10000 - 8000 = 2000.
But we know that the number of PG admissions in college B is equal to the number of PG admissions in college D. So, 2000/2 = 1000.
Therefore, the number of PG admissions in college C is 1000. So, the answer is (b) 1000.
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