Question

In a certain school of 400 students ,the student can stidy newari maithali both or neither. One quarter those who srudy maithali also study newari. The total number who study newari is 20 fewer than those who study maithali only.

a)If the number of students who study both language be x then find the number of student maithali only in terms of x

Answer 1

The number of students studying Maithali only in terms of x, where x is the number of students studying both languages, is found to be M = 4x + 20.

Step-by-step explanation:

Let's denote the number of students studying Maithali only as M, the number studying Newari only as N, and the number studying both languages as x. According to the problem, one quarter of those who study Maithali also study Newari, so the total studying Maithali, which is M + x, is four times the number studying both, which is 4x. We are also told that the number studying Newari, which is N + x, is 20 fewer than those who study Maithali only, so N + x = M - 20. We want to express M in terms of x, and we can do so by rearranging the second equation: M = N + x + 20. Remembering that the number studying Newari (N + x) is also equal to three times the number of those who study both (since N + x = 4x - x = 3x), we can substitute that in:

M = 3x + x + 20

Therefore, the number of students studying Maithali only in terms of x is M = 4x + 20.