Question

The ratio between milk and water in the first container is 5:1 and that
in the second container is 7:2.In what ratio the mixtures of these two
containers should be mixed together so that the quantity of the milk in
the new mixture becomes 75%?​

Answer 1

Answer:

No solution

Step-by-step explanation:

Let milk in first container=$M_{1}$

Let water in first container=$W_{1}$

$\frac{M_{1} }{W_{1} }$=$\frac{5}{1}$

Therefore, $M_{1}$=$5W_{1}$ and $W_{1}$=$\frac{M_{1} }{5} \f$

Let the first container be $C_{1}$

$M_{1} +W_{1} =C_{1}$

$M_{1} +\frac{M_{1} }{5}$=$C_{1}$

$\frac{6M_{1} }{5} =C_{1}$

$M_{1} =\frac{5C_{1} }{6}$

Let milk in second container=$M_{2}$

Let water in second container=$W_{2}$

$\frac{M_{2} }{W_{2} } =\frac{7}{2}$

Thus, $2M_{2}=7W_{2}$ and $W_{2} =\frac{2}{7} M_{2}$

Let the second container be $C_{2}$:

$M_{2} +W_{2} =C_{2}$

$M_{2} +\frac{2}{7} M_{2}=C_{2}$

$\frac{9}{7} M_{2} =C_{2}$

$M_{2} =\frac{7}{9} C_{2}$

Both 7/9 and 5/6, the concentrations of milk in the first and second containers respectively, are greater than 75%. Therefore, it is impossible to produce a mixture in which the quantity of the milk is 75%: the concentration of the mixture could only be between 7/9 and 5/6.