Problem: rs . 6000 is lent out in two parts . one part is lent at 2 % p . a simple interest and the other is lent at 10 % p . a simple interest . the total interest at the end of one year was rs . 450 . find the ratio of the amounts lent at the lower rate and higher rate of interest ?
Rationale: "let the amount lent at 2 % be rs . x amount lent at 10 % is rs . ( 6000 - x ) total interest for one year on the two sums lent = 2 / 100 x + 10 / 100 ( 6000 - x ) = 600 - 3 x / 100 = > 600 - 3 / 100 x = 450 = > x = 1875 amount lent at 10 % = 4125 required ratio = 5 : 11 answer : a"
annotated_formula: divide(divide(subtract(multiply(450, const_100), multiply(6000, 2)), subtract(10, 2)), divide(subtract(multiply(450, const_100), multiply(6000, 2)), subtract(10, 2)))