Find the initial quantity of sugar solution in the given mixture (in litres)?

Question

A mixture contains sugar solution and coloured water in the ratio 4 : 3.
If 14 litres of coloured water is added to the mixture, the ratio becomes 2 : 5.
Find the initial quantity of sugar solution in the given mixture (in litres)?

Answer 1

Let the mixture be X liters, then:
(3/7)*X ====> Amount of coloured solution in the mixture -------- 1
(5/7)*(X+14) ====> Amount of coloured solution in the new mixture ----- 2
2 - 1
(5/7)*(X+14) - (3/7)*X = 14
= (5/7)X + 10 - (3/7)*X = 14
(2/7)*X = 4
X = 4*(7/2) = 14 Litres
Now the initial quantity of the sugar solution in the original mixture = (4/7)*X = (4/7)*14 = 8 Litres.