The combined average number of pens with persons ‘B’

Solution

Let the number of pens with ‘A’ and ‘D’ be ‘x’ and ‘y’, respectively According to the question, Average number of pens with ‘B’ and ‘C’ = {(x + y)/2} × 0.75 So, sum of number of pens with ‘B’ and ‘C’ = {3(x + y)/4} So, sum of number of pens with all 4 persons = (x + y) + {3(x + y)/4} = (7x + 7y)/4 According to the question, (7x + 7y)/16 = 45.5 Or, (x + y) = 45.5 × 16 ÷ 7 = 104 Or, x = y – 16 So, y + y – 16 = 104 y = (104 +16)/2 = 120/2 = 60 So, number of pens with ‘D’ = 60 Number of pens with ‘A’ = 60 – 16 = 44 So, sum of number of pens with ‘B’ and ‘C’ = (44 + 60) × 0.75 = 78 So, average number of pens with ‘B’, ‘C’ and ‘D’ = {(78 + 60)/3} = 138/3 = 46