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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