Calculating Initial Liquid B Quantity

We need to find the initial quantity of liquid B based on the given ratios before and after the operation.

Initial Setup

Let the initial quantities of liquid A and B be $17x$ litres and $18x$ litres, respectively. The total initial quantity is $17x + 18x = 35x$ litres.

Mixture Removal

When 140 litres of the mixture is removed:

• Amount of A removed = $\frac{17}{35} \times 140 = 68$ litres.
• Amount of B removed = $\frac{18}{35} \times 140 = 72$ litres.

Quantities After Removal

• Remaining A = $17x - 68$ litres.
• Remaining B = $18x - 72$ litres.

Adding Liquid B

140 litres of liquid B is added to the remaining mixture:

• New quantity of A = $17x - 68$ litres.
• New quantity of B = $(18x - 72) + 140 = 18x + 68$ litres.

Final Ratio Equation

The new ratio of A to B is 7:8. We set up the equation:

$ \frac{17x - 68}{18x + 68} = \frac{7}{8} $

Solving for x

Cross-multiply and solve the equation:

$ 8(17x - 68) = 7(18x + 68) $

$ 136x - 544 = 126x + 476 $

$ 136x - 126x = 476 + 544 $

$ 10x = 1020 $

$ x = \frac{1020}{10} = 102 $

Initial Quantity of B

The initial quantity of liquid B was $18x$. Substitute the value of $x$:

Initial B = $18 \times 102 = 1836$ litres.