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# The milk and water in two vessels A and B are in the

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Intern
Joined: 11 Sep 2012
Posts: 7
The milk and water in two vessels A and B are in the  [#permalink]

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03 Nov 2018, 19:29
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The milk and water in two vessels A and B are in the ratio 4:3 and 2:3 respectively. In what ratio the liquids in both the vessels be mixed to obtain a new mixture in vessel c consisting half milk and half water?

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Joined: 18 Jun 2018
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Re: The milk and water in two vessels A and B are in the  [#permalink]

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04 Nov 2018, 02:03
Let us take $$1$$ litre of A and $$x$$ litre of B to make $$(1+x)$$ litre of C

Then $$1$$ Litre of A will contain $$\frac{4}{7}$$ Litre of milk and $$\frac{3}{7}$$ Litre of water.

$$x$$ Litre of B will contain $$\frac{2}{5}x$$ Litre of milk and $$\frac{3}{5}x$$ Litre of water.

$$(1+x)$$ of C will contain $$(\frac{4}{7}+\frac{2}{5}x)$$ Litre of milk and $$(\frac{3}{7}+\frac{3}{5}x)$$ Litre of Water

$$\frac{Milk_C}{Water_C}=\frac{\frac{4}{7}+\frac{2}{5}x}{\frac{3}{7}+\frac{3}{5}x}=\frac{1}{1}$$

$$\frac{4}{7}+\frac{2}{5}x=\frac{3}{7}+\frac{3}{5}x$$

$$\frac{1}{7}=\frac{1}{5}x$$

$$x=\frac{5}{7}$$

Ratio of A and B in C $$i.e. \frac{A}{B}= \frac{1}{x}= \frac{1}{\frac{5}{7}}=\frac{7}{5}$$
Re: The milk and water in two vessels A and B are in the &nbs [#permalink] 04 Nov 2018, 02:03
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