The ratio of milk to water in 10 litres of a mixture is 3:2  . If this ratio is to be made 2:3 , then the quantity of water to be added further to the mixture is:

Correct option is C

 Given :

Total mixture = 10 liters

Initial ratio of milk to water = $3:2$

Final ratio of milk to water = $2:3$

to find the quantity of water to be added to achieve the final ratio.

Concept Used : 

​When the amount of milk is constant, the volume of water changes to adjust the ratio.

Solution : 

Let the additional water bexx xliters.

The new ratio can be written as :  $$\frac{Milk}{Water}=\frac{3}{2}$$

Initial quantities of milk and water:
 Milk = $$\frac{3}{5}$$​$\times 10=6\text{liters}$

Water = $$\frac{2}{5}$$​ $\times 10=4\text{liters}$

After adding xxx liters of water:
Milk = $6\text{liters}$ (unchanged)
Water = $4+x\text{liters}$

now, 

$$\frac{6}{4+x}=\frac{2}{3}$$​   

$$6\times3=2\times(4+x)$$​  

x = 5       

The quantity of water to be added is 5 liters. 

The correct answer is option (c) 5 .     

MilkWater=23\frac{\text{Milk}}{\text{Water}} = \frac{2}{3}