Question

Q. There are two vessels - A, and B. A contains water and milk in the ratio $3:2$ and vessel B contains milk and honey in the ratio $5:4$. If one takes equal quantities of solutions from vessels A and B, and pours it into vessel C, what will be the concentration of milk in the new solution?

• A.
  $45.45\%$
• B.
  $42.69\%$
• C.
  $47.78\%$
• D.
  $50\%$

Answer 1

The correct option is C

$47.78\%$
Let the quantity of milk and water in vessel A be $\to 2\times$ and $3\times$ $\left(Total5x\right)$
Let the quantity of milk and honey in Bessel B be $\to 5y$ and $4y$ $\left(total9y\right)$
So, let us take out 45 litres of solution from both A and B.
Quantity of milk taken out from vessel A $=\frac{2x}{(3x+2x)}\times 45=18$
Quantity of milk taken out from vessel B $=\frac{5y}{(4y+5y)}\times 45=25$
Total $\%$ quantity of milk $=\frac{(18+25)}{(45+45)}\times 100=\frac{43}{90}\times 100=47\frac{7}{9}\%$