Question

How many litres of milk solution which contain milk and water in the ratio 5 :3 is added to 42 litres of another milk solution which contain milk to water in the ratio 3:7 to get the ratio of water to milk 5:4

Answer 1

Answer: 11.413 liters

Step-by-step explanation:

Let x liter of  milk solution which contain milk and water in the ratio 5 :3 is added to 42 liters of another milk solution which contain milk to water in the ratio 3:7 to get the ratio of water to milk 5:4.

⇒ $\frac{5}{8}\times 42 + \frac{3}{10} \times x = \frac{5}{9} ( 42 + x)$

$\frac{210}{8} + \frac{3x}{10} = \frac{210+5x}{9}$

$\frac{1050}{40} + \frac{12x}{40} = \frac{210+5x}{9}$

$\frac{1050+12x}{40} = \frac{210+5x}{9}$

$9450+108x = 8400+200x$

$9450+108x -200x = 8400-9450$

$-92x=-1050$

$x=11.4130434783\approx 11.413$

Hence, Required quantity of milk solution which contain milk and water in the ratio 5 :3 is 11.413 liter.