There are 2 solutions of acid and water in the ratio 3:5 and 1:3 respectively. Equal quantities of 2 solutions are mixed together and out of this solution, 704 ml is taken out and 88 ml of water is added, find the ratio of acid to water in the resulting solution.
options : a) 4:11 b) 6:11 c) 5:13 d) 7:13
I know that answer is 5:13 but I am unable to reach a proper explanation. Can someone please explain with steps, how we get 5:13?
Answers
Answer:
Option (C) 5:13 is correct answer.
Step-by-step explanation:
Given:
The ratio of acid to water in the first solution = 3 : 5
The ratio of acid to water in the second solution = 1 : 3
Equal quantities of these two solutions are mixed in a vessel. From this resulting solution, 704 ml is taken out and mixed with 88 ml of water.
Calculation:
The ratio of acid to water in the first solution = 3 : 5 ---(1)
The ratio of acid to water in the second solution = 1 : 3 ---(2) × 2
Multiply by 2 in equation (2) to make the total quantity of first and second solution the same
The ratio of acid to water in the second solution = 2 : 6
⇒ The ratio of acid to water if both solution mixed in new vessel = (3 + 2) : (5 + 6) = 5 : 11
If 704 ml of solution is taken out in the mixed solution
⇒ Quantity of acid taken out from the mixed solution = 704 × (5/16) = 220 ml
⇒ Quantity of water taken out from the mixed solution = 704 – 220 = 484 ml
Now, 88 ml water is added to this mixture
⇒ New quantity of water = 484 + 88 = 572 ml
∴ Ratio of acid to water = 220 : 572 = 5 : 13