Q. P liters mixture of milk and water, where milk is twice as that of water. If Q liters of water are added to the mixture, then water becomes 75% of milk. If 3.5Q liters of mixture is removed and replaced by 2Q liters of milk, then quantity of milk in mixture can be_____liters
I. 4Q
II. 6Q
III. 2P/3
A. I only
B.II only
C.III only
D.I and III only
E.II and III only
Ans: I and III only
Sol:
Initial ratio of milk and water in mixture = 2:1
Amount of milk in Mixture = 2P/3
Amount of water in mixture = P/3
Now,
2P/3 / (P/3 + Q) = 4/3
2P = 4P/3 + 4Q
2P/3 = 4Q
Value of P = 6Q
Now, amount of water in Mixture = 2P/3 = 2 x
6Q/3 = 4Q
Amount of milk in Mixture = 3/4 x 4Q = 3Q
After removal of 3.5Q liters mixture and adding
2Q liters water
Amount of milk in mixture (4Q – 4/7 x 3.5Q + 2Q)
= 4Q = 2P/3
Only I and III follows
Hence answer is option D.