In a container, two types of liquids P and Q are in the ratio of 3 : 7. If 10 litres mixture is drawn off from the container and filled with 6 litres of liquid Q, then the ratio of P and Q becomes 1 : 3. What was the original quantity (in litres) of mixture?

Let original quantity of mixture = $$100x$$ litres

=> Quantity of P = $$30x$$ and Q = $$70x$$ litres

If 10 litres mixture is drawn, => quantity of P taken out = 3 litres and Q = 7 litres

6 litres of liquid Q is added, thus new ratio

=> $$\frac{30x-3}{70x-7+6}=\frac{1}{3}$$

=> $$\frac{30x-3}{70x-1}=\frac{1}{3}$$

=> $$90x-9=70x-1$$

=> $$90x-70x=9-1$$

=> $$20x=8$$

=> $$x=\frac{8}{20}=0.4$$

$$\therefore$$ Original quantity of mixture = $$100\times0.4=40$$ litres

=> Ans - (D)