Two solutions A and B contain spirit and water in the ratio 5:6 and 7:4 respectively. They are mixed in the ratio 3:5 in a vessel. In 220 ml of the solution in the vessel, how much water(in ml) should be added to make it a solution in which the ratio of spirit and water is 25:27? A. 40 B. 35 C. 45 D. 50
Answers
Answer:
Let x quantity of solution A be mixed with y quantity of solution B to form the new mixture. Then since the contents of A and B are mixed in the ratio 3:4,
x:y = 3:4
⇒ y = 4x/3
Given, solution: water in solution A = 5 : 7
∴ Spirit content in x = 5x/12
and Water content in x =
In solution B, Spirit : water = 3 : 5
∴ Using (1),
Spirit content in y = 3y/8 = 3/8 . 4x/3 = 3.4.x/3.8 = x/2
and Water content in y = 5y/8 = 5/8 .4x/3 =
(2) + (4) give
Total spirit content of the mixture = 5x/12 + x/2 = (5x + 6x)/12 = 11x/12 ……..…..(6)
(3) + (5) give
Total water content of the mixture = 7x/12 + 5x/6 = (7x + 10x)/12 = 17x/12 ………(7)
From (6) and (7),
Ratio of spirit to water in the new mixture
= 11x/12 ÷ 17x/12 = (11x/12) (12/17x)
= 11/17 or 11:17 (Answer)
which is 40