in a hostel , the number of students decreased by 15 % and the price of food increased by 20 % over the previous year . if each student consumes the same amount of food then by how much should the consumption of food be cut short by every student , so that the total cost of the food remains the same as that of the previous year ?
"cost of food ( c ) = food consumed per student ( f ) * number of students ( n ) * price of food ( p ) originally , c = fnp when number of students decrease by 15 % , and the price of food increases by 20 % , c = f ( new ) * ( 0.85 n ) * ( 1.2 p ) = > f ( new ) = f / ( 0.85 * 1.2 ) = > f ( new ) = 0.9804 f therefore the new cost of food must be 98.04 % of the old cost , or the cost of food must decrease by 1.96 % ( option e )"
multiply(subtract(const_1, divide(multiply(const_100, const_100), multiply(subtract(const_100, 15), add(const_100, 20)))), const_100)