Question

The ratio of milk and water in a mixture is 2:1. How much part of the mixture should be replaced by water so that ratio of milk and water is 5:3?

Answer 1

Let the -

• litres of milk and water present in the ratio 2:1 be x and the part of the mixture to be replaced by mixture so that ratio of milk and water become 5:3 is also x.
• Replaced mixture = y

Total part = 2 + 1 = 3

The ratio of milk and water = 2:1

Now,

→ Amount of milk in new mixture = 2x/3 - 2y/3

→ Amount of water in new mixture = 1x/3 - 1y/3

According to question,

$\implies\:\sf{\dfrac{ \frac{2x}{3} \: - \: \frac{2y}{3} }{ \frac{1x}{3} \: - \: \frac{1y}{3} } \: = \: \dfrac{5}{3}}$

$\implies\:\sf{\dfrac{ \frac{2x \: - \: 2y}{3}}{ \frac{1x \: - \: 1y}{3}} \: = \: \dfrac{5}{3}}$

$\implies\:\sf{\dfrac{2x\:-\:2y}{1x\:-\:1y}\:=\:\dfrac{5}{3}}$

$\implies\:\sf{3(2x\:-\:2y)\:=\:5(x\:-\:y)}$

$\implies\:\sf{6x\:-\:6y\:=\:5x\:-\:5y}$

$\implies\:\sf{6x\:-\:5x\:=\:-\:5y\:+\:6y}$

$\implies\:\sf{1x\:=\:1y}$

$\implies\:\sf{\dfrac{x}{y}\:=\:\dfrac{1}{1}}$

•°• Mixture should replace 1/1 part of the water. So, that the ratio of milk and water becomes 5:3

Answer 2

Answer:

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