Due to academic pressure, students who were enrolled in all three sports were asked to withdraw from one of the three sports. After the withdrawal, the number of students enrolled in G was six less than the number of students enrolled in L, while the number of students enrolled in K went down by one. After the withdrawal, how many students were enrolled in both G and K?
Explanation:
Out of 4 students who are enrolled in all the three, suppose ‘a’ students dropped out of L and ‘b’ students dropped out of K. Therefore the number of students who dropped out of G = 4 - a - b. Therefore we have the following:
If the number of students enrolled in K reduced by 1 that means out of the 4 students who had enrolled in all the three, one student dropped out of K i.e. b = 1.
Now, if the number of students enrolled in G was 6 less than the number of students enrolled in L, we have the following:
(7 + w + a + 6 − w + b) + 6
= 6 − w + b + 9 − a − b + 8
∴19 + a + b = 23 − w − a
∴2a + b + w = 4
Since b = 1, the only solution for the equation 2a + b + w = 4 is a = 1, b = 1 and w = 1.
Now both the questions can be answered.
The required number of students = w + a = 2.
Answer: 2
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