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Quantitative Reasoning – Practice – Solve the ‘mixture’ question in 3 ways!

PSA_PRACTICE_QNR50. Let us assume, the percentage of liquid A is ‘x’ in the resultant mixture. By weight, liquid A makes up 8 percent of solution R and 18 percent of solution S. If 3 grams of solution R are mixed with 7 grams of solution S,then liquid A accounts for what percent of the weight of the resulting solution?

A 10%
B 13%
C 15%
D 19%
E 26%

Ans:

Method 1
We can solve the question using the below representation:

Individual percentages are written in one; and resultant percentage ‘x’ is presented in the middle.

 

PSA_PRACTICE_QNR50

 

(18-x)/(x-8) = 3/7

=>126-7x = 3x -24
=>10x= 150
=>x=15

Method 2

3 grams of solution R contains 8% liquid A

8% of 3= 0.24

Similarly, 7 grams of solution S contains 18% liquid A

18% of 7= 1.26

Total weight of the mixture = 3+ 7 = 10 gm.

Total weight of liquid A in the mixture= 0.24 + 1.26 = 1.5

Percentage of liquid A in the mixture = (1.5/10) * 100 = 15%

Method 3

The percentage of liquid A would have been exactly in the MIDDLE if both the solutions were mixed in equal quantities; in that case the percentage would have been average of 8 and 18
i.e 13. But that is not the case here. Quantity of solution S is more ( 7 gm > 3 gm), thus the average would tilt more towards 18 than 8. Thus, the value should be above 13 but definitely
less than 18. Only option C can fit in.

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