jackfr2 wrote:
A bucket contains a mixture of two liquids A & B in the proportion 5 : 3. If 16 litres of the mixture is replaced by 16 litres of liquid B , then the ratio of the two liquids becomes 3 : 5. How much of the liquid B was there in the bucket ?
(A) 12 litres
(B) 15 litres
(C) 18 litres
(D) 6 litres
(E) 24 litres
We can use ALLIGATION.
Let:
S = the original solution
B = the 16 liters of pure B
M = the final mixture
Alligation can be performed only with percentages or fractions.
Step 1: Convert the ratios to FRACTIONS with the same denominator.S --> Since A:B = 5:3, \(\frac{B}{total} = \frac{3}{8}\)
B --> \(\frac{B}{total} = \frac{{16}}{{16}} = \frac{8}{8}\)
M --> Since A:B = 3:5, \(\frac{B}{total} = \frac{5}{8}\)
Step 2: Plot the 3 numerators on a number line, with the numerators for S and B on the ends and the numerator for the mixture in the middle.S 3------------5-----------8 B
Step 3: Calculate the distances between the numerators.S 3-----
2-----5-----
3-----8 B
Step 4: Determine the ratio in the mixture.The ratio of S to B is equal to the RECIPROCAL of the distances in red.
S:B = 3:2 =
24:16.
The ratio in blue indicates that the mixture is composed of 24 liters of original solution and 16 liters of pure B, implying that the total volume in the bucket = 40 liters.
Since B constitutes \(\frac{3}{8}\) of the original 40 liters in the bucket, we get:
\(\frac{3}{8} * 40 = 15\) liters
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