Four equal jugs are filled with the mixture of sprit and water. The ratio of sprit to water in four jugs is 1:3, 3:5, 5:11 and 7:9. The mixture of the four jugs is emptied into a single vessel. What is the proportion of sprit to water in the vessel?

11:21

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Solution

The correct option is A
11:21

Let x (in ml) be the volume of each jug.

$\begin{matrix} J u g & 1^{s t} & 2^{n d} & 3^{r d} & 4^{t h} S : W & 1 : 3 & 3 : 5 & 5 : 11 & 7 : 9 S & \frac{1}{4} x & \frac{3}{8} x & \frac{5}{16} x & \frac{7}{16} x W & \frac{3}{4} x & \frac{5}{8} x & \frac{11}{16} x & \frac{9}{16} x \end{matrix}$

$\frac{(\frac{1}{4} x + \frac{3}{8} x + \frac{5}{16} x + \frac{7}{16} x)}{(\frac{3}{4} x + \frac{5}{8} x + \frac{11}{16} x + \frac{9}{16})} = \frac{(\frac{22}{16})}{(\frac{42}{16})} = \frac{22}{42} = \frac{11}{21}$

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Four equal jugs are filled with the mixture of sprit and water. The ratio of sprit to water in four jugs is 1:3, 3:5, 5:11 and 7:9. The mixture of the four jugs is emptied into a single vessel. What is the proportion of sprit to water in the vessel?

The correct option is A 11:21 Let x (in ml) be the volume of each jug. Jug1st2nd3rd4thS:W1:33:55:117:9S14x38x516x716xW34x58x1116x916x (14x+38x+516x+716x)(34x+58x+1116x+916)=(2216)(4216)=2242=1121