Question 69

A container has 30 litres of milk, from which 3 litres of milk is taken out and replaced with water. The process is done three times. What is the final ratio of the water and the milk in the container?

Solution

As we know, 

Final Quantity = Initial Quantity $$\times\ \left(1-\frac{r}{q}\right)^n$$

(where r = quantity taken out , Q = capacity of Beaker and n = number of times process repeated)

Given, 

Initial quantity / Q = 30 lt

R = 3 lt

Now,

$$30\times\ \left(1-\frac{3}{30}\right)^3=30\times\ \frac{9}{10}\times\ \frac{9}{10}\times\ \frac{9}{10}$$

= 21.87 lt

Remaining is water = 30 = 21.87 = 8.13 lt

The Required ratio = 8.13 : 21.87 

= 271 : 729

Hence, Option D is correct.


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