g106 wrote:
15 lts are taken of from a container full of liquid A and replaced with Liquid B. Again 15 more lts of the mixture is taken and replaced with liquid B. After this process, if the container contains Liquid A and B in the ratio 9:16,What is the capacity of the container?
A:45
B:25
C:37.5
D:36
E:42
Given:
1. 15 lts are taken of from a container full of liquid A and replaced with Liquid B.
2. Again 15 more lts of the mixture is taken and replaced with liquid B.
3. After this process, if the container contains Liquid A and B in the ratio 9:16,
Asked: What is the capacity of the container?
Let the capacity of the container be V ltr
After first iteration,
Liquid A = V - 15 lts
Liquid B = 15 lts
Ratio A: B = (V-15)/15
Ratio A: A+B = (V-15)/V
Ratio B: A+B = 15/V = [1-(V-15)/V]
After second iteration
Liquid A = (V-15) - 15(V-15)/V = (V-15) (1 -15/V) = (V-15)^2/V
Liquid B = 15 - 15*15/V + 15 = 30 - 225/V = 30V -15^2/V
Ratio A: A+B = (V-15/V)^2 = 9/25
V-15/V = 3/5
V = 5/2*15 = 37.5 ltr
IMO C
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