Problem: cp of 3 buffaloes are $ 30,000 . by selling 1 at a loss of 15 % and other at a profit of 19 % , he foundthat sp of both buffaloes is the same . find the cp of each ?
Rationale: let the c . p of 1 st buffalo = x ∴ c . p of 2 nd buffalo = 30,000 - x s . p of 1 st buffalo = ( 100 - loss % ) - - - - - - - - - - - - - - - - - - - x c . p 100 s . p = 100 - 15 x - - - - - - - - - - - = 85 x / 100 100 s . p of 2 nd buffalo = ( 100 - profit % ) - - - - - - - - - - - - - - - - - - - - - x c . p 100 s . p = ( 100 + 19 ) ( 30,000 - x ) 119 ( 30,000 - x ) - - - - - - - - - - - - - - - - - - - - = - - - - - - - - - - - - - - - - 100 100 s . p of 1 st buffalo = s . p of 2 nd buffalo 85 x / 100 = 119 ( 30,000 - x ) / 100 ⇒ 85 x = 119 ( 30,000 - x ) ⇒ 85 x = 3 , 570,000 - 119 x ⇒ 85 x + 119 x = 3 , 570,000 ⇒ 204 x = 3 , 570,000 ⇒ x = 3 , 570,000 / 204 ⇒ x = $ 17,500 c . p of 1 st buffalo = $ 17,500 c . p of 2 nd buffalo = 30,000 - 17,500 = $ 12,500 e
annotated_formula: subtract(multiply(multiply(3, const_100), sqrt(const_100)), divide(multiply(multiply(3, const_100), sqrt(const_100)), add(divide(add(divide(19, const_100), const_1), subtract(const_1, divide(15, const_100))), const_1)))