Question

two vessel contain milk and water in the ratio 7:5 and 7:9 if both are mixed in ratio 1:1 find the ratio of milk and water in new mixture

Answer 1

SOLUTION

GIVEN

Two vessel contain milk and water in the ratio 7:5 and 7:9 if both are mixed in ratio 1:1

TO DETERMINE

The ratio of milk and water in new mixture

EVALUATION

Here it is given that two vessel are mixed in ratio 1 : 1

Let P unit of first vessel is mixed with P unit of second vessel

In the first vessel

Ratio of milk and water = 7 : 5

$\displaystyle \sf{} Amount \: of \: milk = P \times \frac{7}{7 + 5} = \frac{7P}{12}$

$\displaystyle \sf{} Amount \: of \: water = P \times \frac{5}{7 + 5} = \frac{5P}{12}$

In the second vessel

Ratio of milk and water 7 : 9

$\displaystyle \sf{} Amount \: of \: milk = P \times \frac{7}{7 + 9} = \frac{7P}{16}$

$\displaystyle \sf{} Amount \: of \: water = P \times \frac{9}{7 + 9} = \frac{9P}{16}$

Now two vessel are mixed

Then

Total amount of milk

$= \displaystyle \sf{} \frac{7P}{12} + \frac{7P}{16}$

$= \displaystyle \sf{} \frac{28P + 21P}{48}$

$= \displaystyle \sf{} \frac{49P}{48}$

Total amount of Water

$= \displaystyle \sf{} \frac{5P }{12} + \frac{9P}{16}$

$= \displaystyle \sf{} \frac{20P + 27P}{48}$

$= \displaystyle \sf{} \frac{47P}{48}$

Hence the required ratio of milk and water is

$= \displaystyle \sf{} \frac{49P}{48} \: : \: \frac{47P}{48}$

$= \sf{}49 \: : \: 47$

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