A container holds a mixture of three liquids A, B, and C in ratio 2:3:5. If 6 liters of liquid A, 12 liters of liquid B, and a certain amount of liquid C are added to the container, the new ratio of liquids A, B, and C becomes 3:5:8. Find the quantity (in liters) of liquid C added.

Correct option is C

Given:

Initial ratio of liquids A : B : C = 2 : 3 : 5
Added: 6 L of A, 12 L of B, and xL of C
New ratio = 3 : 5 : 8

Solution:

Let initial amounts be 2k, 3k, 5k. ​

​$$\frac{2k + 6}{3k + 12} = \frac{3}{5}$$​​

5(2k + 6) = 3(3k + 12)

10k + 30 = 9k + 36

k = 6​

Use k = 6 to find x:

​$$\frac{5k + x}{2k + 6} = \frac{8}{3}$$​​

A after addition: 2k + 6 = 12 + 6 = 18
C after addition: 5k + x = 30 + x

​$$\frac{30 + x}{18} = \frac{8}{3}$$​​

30 + x = 48 

x = 18

Thus, the quantity of liquid C added is 18 liters.