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12,9,7,3,4,6,?

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Number Puzzle #143

Which number replaces the question mark?

12,9,7,3,4,6,?
12,9,7,3,4,6 which number replaces

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Answer seems to be 9

as number in upper line = 3(middle line) + opposite number in bottom line

Vessel with water and syrup

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vessel-with-water-and-syrup
A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?

A. 1/3
B. 1/4
C. 1/5
D. 1/7

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Lets assume that we take x part of the mixture out, and assuming uniform distribution of water and syrup, we can say out of the x part, 3x/8 was water and 5x/8 was syrup, now on replacing this x part by water, both water and syrup part should become equal, we can form the below equation

Water Part = Syrup part
3 – 3x/8 + x = 5 – 5x/8
x +2x/8 = 2
5x/4 = 2
x = 8/5

initially total quantity was 8(i.e. 3+5), and we should take out 1/5th part out and replace it with water to make both equal.

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