Question

A jar contains a mixture of two liquids A and B in the ratio \(4:1\). When \(10\) liters of the mixture is taken out and \(10\) liters of liquid B is poured into the jar, the ratio becomes \(2:3\). How many liters of liquid A was contained in the jar initially?

• A. \(12\) l
• B. \(16\) l
• C. \(20\) l
• D. \(24\) l

Hint:

When some mixture is removed, each ingredient is removed in exactly the same ratio as present in the mixture.

Answer 1

The Correct Option is B

Concept: When a quantity of mixture is removed, both liquids are removed in the same proportion as they exist in the mixture. This principle is frequently used in replacement and allegation problems.

Step 1: Assume the initial quantities.
Let the initial quantities be \[ A=4x,\qquad B=x. \] Total mixture \[ =5x. \]

Step 2: Determine the quantities removed.
Since the ratio is \(4:1\), from \(10\) liters removed: \[ A\text{ removed} = 10\times\frac45 = 8 \text{ liters}. \] \[ B\text{ removed} = 10\times\frac15 = 2 \text{ liters}. \] Remaining: \[ A=4x-8, \] \[ B=x-2. \]

Step 3: Add 10 liters of liquid B.
New quantity of B: \[ x-2+10=x+8. \] Thus new ratio is \[ \frac{4x-8}{x+8} = \frac23. \]

Step 4: Solve the equation.
\[ 3(4x-8)=2(x+8) \] \[ 12x-24=2x+16 \] \[ 10x=40 \] \[ x=4. \] Therefore \[ A=4x=16. \] Hence, \[ \boxed{16\text{ liters}} \] Therefore the correct option is \[ \boxed{(B)} \]