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(D) Let the volumes of the three vessels be $2x, 3x$,and $5x$ respectively.In the first vessel (volume $2x$),the ratio of water to milk is $1: 3$. Wat

Vedclass · Accepted Answer

$481: 219$

Vedclass · Answer

(D) Let the volumes of the three vessels be $2x, 3x$,and $5x$ respectively.In the first vessel (volume $2x$),the ratio of water to milk is $1: 3$. Water $= 2x 	imes \frac{1}{4} = 0.5x$,Milk $= 2x 	imes \frac{3}{4} = 1.5x$.In the second vessel (volume $3x$),the ratio of water to milk is $2: 3$. Water $= 3x 	imes \frac{2}{5} = 1.2x$,Milk $= 3x 	imes \frac{3}{5} = 1.8x$.In the third vessel (volume $5x$),the ratio of water to milk is $2: 5$. Water $= 5x 	imes \frac{2}{7} = \frac{10}{7}x \approx 1.428x$,Milk $= 5x 	imes \frac{5}{7} = \frac{25}{7}x \approx 3.571x$.Total water $= 0.5x + 1.2x + \frac{10}{7}x = 1.7x + \frac{10}{7}x = \frac{11.9x + 10x}{7} = \frac{21.9x}{7} = \frac{219x}{70}$.Total milk $= 1.5x + 1.8x + \frac{25}{7}x = 3.3x + \frac{25}{7}x = \frac{23.1x + 25x}{7} = \frac{48.1x}{7} = \frac{481x}{70}$.Ratio of milk to water $= \frac{481x/70}{219x/70} = 481: 219$.

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