A vessel contains a mixture of P and Q in the ratio of 5 : 3. 16 liters of this mixture is taken out and 5 liters of P is poured in. The new mixture has a ratio of P to Q as 11 : 6. Find the total original quantity of mixture.

Question: A vessel contains a mixture of P and Q in the ratio of 5 : 3. 16 liters of this mixture is taken out and 5 liters of P is poured in. The new mixture has a ratio of P to Q as 11 : 6. Find the total original quantity of mixture.

Solution:
Let,
Original Quantity of P = 5x
Original Quantity of Q = 3x

The quantity of P and Q in 16 liters of the mixture:
Quantity of P = (16 × 5x)/8x = 10 liters
Quantity of Q = (16 × 3x)/8x = 6 liters

Now,
5 liters of P poured in so the Quantity of P will be = 5x - 10 + 5 liters
= 5x - 5 liters

ATQ,
(5x - 5)/(3x - 6) = 11/6
⇒ 6(5x - 5) = 11(3x - 6)
⇒ 30x - 30 = 33x - 66
⇒ 3x = 36
∴ x = 12

So total mixture originally = 8x = 8 × 12 = 96 liters