An exhausted zeolite bed was revived by 250 L of NaCl solution containing 50 g/L of NaCl solution. How many litres of hard water of hardness 250 ppm can be softened on the zeolite bed?

Dear student 

V1 = Vol of Hard water 
V2 = Vol of Nacl
solution containing xgL−1 used for the regeneration of the zeolite. Then hardness (H) is given by: 
Hardness(H)=50*x*V2*10^3 / 58.3×V1
Ew of CaCO3 = 50
Mw of NaCl= 85.5 
In the prioblem x=50gL−1, V2=250L, H=250p , 
We need to find V1
So, 250=50×50×250×10^3 / 58.5×V1 
∴V1=42735L