A bottle is filled with a mixture of water and syrup in ratio 2 : 5, respectively. How much of the mixture must be replaced with water so that the mixture has half water and half syrup? 

Correct option is D

Given:

Initial water : syrup = 2 : 5

Water = $$\frac 27$$​, Syrup =$$\frac 57$$​​

Solution:

Suppose, Total = 1 litre 

Let x litre be removed and replaced with water.

Water removed = $$\frac 27$$​x

Syrup removed = $$\frac 57$$​x

Water after replacement = $$\frac27 - \frac 27x + x = \frac27 + \frac57x$$​​

Syrup after replacement =$$\frac57 - \frac57$$​x

To make equal parts:

​$$\frac27 + \frac57x = \frac57 - \frac57x$$​​

​$$\frac57x + \frac 57x = \frac57 - \frac27 = \frac37$$​​

​$$\frac{10}7$$​x = $$\frac 37$$​​

x = $$\frac 3{10}$$​​

∴ $$\frac 3{10}$$​of the mixture must be replaced with water.