Question

Q41. A vessel contains mixture of milk and water in the ratio of 3:8. 1/4 th of the mixture taken out and replaced with mango juice and this process repeated one more time. If the quantity of milk in final mixture is 40.5 liters, then find the initial quantity of water in the mixture?​

Answer 1

Answer:

108 lits.

Step-by-step explanation:

Let the vessel contains x lits. of milk and water mixture in the ratio of volume 3:8.

If 1/4th of the mixture is taken out, the remaining mixture volume will be (x-x/4) = 3x/4 lits.

Now, the volume of milk in the mixture is given by  

$\frac{3x}{4}.\frac{3}{3+8} =\frac{9x}{44}$ lits. ....... (1)

And the volume of water in the mixture is given by  

$\frac{3x}{4}.\frac{8}{3+8} =\frac{6x}{11}$ lits. ......... (2)

It is clear that if you add mango juice to the above mixture for once or twice, the volume of milk does not change.

As per given condition, the volume of milk in the final mixture from equation (1)

$\frac{9x}{44}=40.5$ lits.

⇒ x=198 lits.  

Now, from equation (2), the initial quantity of water in the mixture will be,

$\frac{6*198}{11}$lits.

=108 lits (Answer)