# XAT 2015 Quant & DI Q7: Mixtures

This aptitude question appeared as a part of the quantitative reasoning and data interpretation section of the XAT 2015. Question 7 of a total of 33 questions that appeared in this section in XAT 2015. This one is a medium level difficulty question and tests the concept of compound mixtures.

## Question

Product M is produced by mixing chemical X and chemical Y in the ratio of 5 : 4. Chemical X is prepared by mixing two raw materials, A and B, in the ratio of 1 : 3. Chemical Y is prepared by mixing raw materials, B and C, in the ratio of 2 : 1. Then the final mixture is prepared by mixing 864 units of product M with water. If the concentration of the raw material B in the final mixture is 50%, how much water had been added to product M?

1. 328 units
2. 368 units
3. 392 units
4. 616 units
5. None of the above

Correct Answer      Choice B. 368 units of water has been added to product M to get the final mixture.

• #### Decode the given data

M is produced by mixing chemical X and chemical Y in the ratio 5 : 4

Hence, $\frac{5}{9}\\$th of product M is chemical X and $\frac{4}{9}\\$th of product M is chemical Y.

Chemical X has A and B in the ratio 1 : 3.
So, $\frac{3}{4}\\$th of X is B.
Therefore, fraction of B in product M from chemical X = $\frac{5}{9}\\$×$\frac{3}{4}\\$

Chemical Y has B and C in the ratio 2 : 1.
So, $\frac{2}{3}\\$rd of Y is B.
Therefore, fraction of B in product M from chemical Y = $\frac{4}{9}\\$×$\frac{1}{3}\\$

Adding the two, the fraction of B in Product M
= $\frac{5}{9}\\$×$\frac{3}{4}\\$ + $\frac{4}{9}\\$×$\frac{2}{3}\\$
= $\frac{77}{108}\\$

• #### Compute the amount of water added

The final product is obtained by mixing 864 units of product M with water.
In 864 units of Product M, amount of B = 864×$\frac{77}{108}\\$ = 616

In the final mixture, concentration of B is 50%.

Therefore, the total quantity of final mixture = 616 × 2 = 1232
Water added = 1232 – 864 = 368

The correct answer is Choice B.

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