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Question:

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.

Explanation:

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 2/3^rd of the total mixture.

⇒ Total volume of the mixture = 3/2 × 8x = 12x ml and volume of water = 1/3^rd 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).