Problem: a mixture contains milk and water in the ratio 5 : 2 . on adding 10 liters of water , the ratio of milk to water becomes 5 : 3 . the quantity of milk in the original mixture is ?
Rationale: "milk : water = 5 : 2 5 x : 2 x + 10 = 5 : 3 3 [ 5 x ] = 5 [ 2 x + 10 ] 15 x = 10 x + 50 15 x - 10 x = 50 x = 10 the quantity of milk in the original mixture is = 5 : 2 = 5 + 2 = 7 7 x = 70 short cut method : milk : water = 5 : 2 after adding 10 liters of water milk : water = 5 : 3 milk is same but water increse 10 liters then the water ratio is increse 1 parts 1 part - - - - - > 10 liters the quantity of milk in the original mixture is = 5 : 2 = 5 + 2 = 7 7 parts - - - - - > 70 liters ( answer is = 70 ) short cut method - 2 : for only milk problems milk : water 5 : 2 5 : 3 milk ratio same but water ratio 1 part incress per 10 liters 1 part of ratio - - - - - - - > 10 liters 7 part of ratio - - - - - - - > 70 liters c )"
annotated_formula: divide(multiply(10, divide(const_2.0, const_3.0)), subtract(divide(3, add(5, 2)), multiply(divide(2, add(5, 2)), divide(2, 5))))