XAT 2018 — QA & DI Question 5
A mixture comprises water and liquids A and B. The volume of water is 1/3rd of the total mixture and the volume of liquids A and B are in the ratio 5:3. To remove the water, the mixture is passed through a porous medium which completely absorbs the water and partially absorbs liquid A. Altogether this porous medium absorbs 200 ml of the initial mixture. If the ratio of volume of liquids A and B in the residual concentrated mixture becomes 7:9 then find the volume of water absorbed by the porous medium.
Answer & solution
- A
60 ml
- B
200/3 ml
- C
80 ml
- D
100 ml
120 ml
Let the volume of liquid A and B in the initial mixture be 5x and 3x ml.
∴ Total volume of A and B = 8x ml, this is 2/3rd of the total mixture.
⇒ Total volume of the mixture = 3/2 × 8x = 12x ml and volume of water = 1/3rd of 12x i.e., 4x ml.
∴ Volume of water, liquid A and liquid B in the mixture will be 4x, 5x and 3x respectively.
When this mixture passes through the porous material whole of water and part of liquid A is absorbed. B is not absorbed by the porous material.
Now, since the ratio of volume of liquids A and B in the residual concentrated mixture becomes 7:9
⇒ (Remaining volume of A) : (3x) = 7 : 9
⇒ Remaining volume of A = 7x/3 ml.
∴ Volume of A absorbed = 5x – 7x/3 = 8x/3
Volume of water absorbed = 4x ml
⇒ 4x + 8x/3 = 200
⇒ x = 30.
∴ Volume of water absorbed = 4x = 120 ml.
Hence, option (d).