The average of 39% of A and 42% of B is equal to three-fifths of the difference of A and B. Find B as a percentage of A.

Explanation

Given: The average of 39% of A and 42% of B is equal to three-fifths of the difference of A and B. Concept used: Average = Sum of elements/Number of elements Calculation: [A × (39/100) + B × (42/100)]/2 = (A - B) × (3/5) ⇒ [(39A + 42B)/100]/2 = (3A - 3B)/5 ⇒ ( 39A + 42B)/200 = (3A - 3B )/5 ⇒ ( 39A + 42B)/40 = (3A - 3B ) ⇒ 39A + 42B = 120A - 120B ⇒ 42B + 120B = 120A - 39A ⇒ 162 B = 81A ⇒ B/A = 81/162 So, ratio of A and B = 81 : 162 or 1 : 2 So, B = (1/2) × 100 of A or 50% of A ∴ Required answer is 50%.