Assume you have 1000 ml M out of which 200 ml is calcium chloride leading to 20% concentration.
Remove 3/4 of M, which will mean now we have (1000/4) = 250 ml M out of which (200/4) = 50 ml is calcium chloride leading to 20% concentration.
To have 37.5% concentration in 2000 ml we should have 750 ml in 2000 ml.

2000 ml is taken as question says we need twice the volume of solution M in final solution P.
(One small assumption here that twice the volume of P meant twice from original quantity of M and not after removing 3/4th)

In this remove remaining quantities from solution M => 750 - 50 = 700 ml & 2000 - 250 = 1750 ml
These quantities need to come from solution N.

Concentration of calcium chloride in solution N = (700/1750)*100 = 40
Answer C

X=Concentration of Ca in N
M=Volume of solution M
N=volume of solution N
P=volume of solution P
Remove three-fourths of M and then add N to create P, P=2M
=> 1/4 M +N=2M=>N=7/4 M
Concentration Of Ca in P=0.375
1/4 M*0.2 + X *7/4M =3/8 *2M=>x=0.4

Anser is C
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weighted average method
Volume of initial solution M is 1/4 and concentration is 20%.But since final volume is 2 times, the volume of remaining M as a part of P is 1/4*1/2=1/8 so 1 part
Volume of solution P is 1 or8 parts and concentration is 37.5%
Volume of N is 1-1/8=7/8 , that is 7 parts and volume be v.

M...................P......N
1...................8.......7
20%..........37.5%...v
So \(v=P + \frac{(37.5-20)}{7}=37.5+\frac{17.5}{7}=37.5+2.5=40%\)

C
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let x=calcium chloride concentration of solution N
.2*(1/4)+x*(7/4)=.375*2
x=.4=40%
C

We can let amount of solution M = 20 liters, so it has 0.2 x 20 = 4 liters of calcium chloride. We also remove ¾ x 20 = 15 liters of M, which includes ¾ x 4 = 3 liters of calcium chloride. Thus, we have 5 liters of M left (which includes 1 liter of calcium chloride), and we have to add 35 liters of solution N to make 40 liters of solution P (recall that solution P is double the amount of solution M).

We can x = the percent of calcium chloride in solution N and create the equation:

(1 + x/100 * 35)/40 = 0.375

1 + 35x/100 = 15

35x/100 = 14

35x = 1400

x = 40

Alternate Solution:

Assume we start with 4 liters of 20% solution. We will remove ¾ of it, which is 3 liters of 20% solution. Now we add 7 liters of unknown concentration x, and the result is 8 liters of 37.5% solution. Note that we need to end with twice the volume of what we started with, so we end with 8 liters of solution. We can create the following equation:

4(0.20) - 3(0.20) + 7x = 8(0.375)

0.8 - 0.6 + 7x = 3

7x = 2.8

x = 0.40, or 40%

Answer: C
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