Question
There are two classrooms, A and B. If 20 students are
shifted from A to B, the number of students in each room becomes the same. If 30 students are sent from B to A, the number of students in A becomes thrice the number of students in B. Find the number of students in each classroom.Solution
Let students in A = a, in B = b. From first condition: a - 20 = b + 20 => a - b = 40 ...(i) From second condition: a + 30 = 3(b - 30) => a + 30 = 3b - 90 => a - 3b = -120 ...(ii) Subtracting (ii) from (i): (a - b) - (a - 3b) = 40 - (-120) => 2b = 160 => b = 80 Substitute b in (i): a - 80 = 40 => a = 120
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