Write the total milliequivalents of CO32- in 100 ml as given:
that would be: 100/50 = 2.
After neutralizing 25 ml,
meq. of co3 gets remained = (200/25)*8.2/50 = 1.3
thus CACO3 resent in 100 ml water is = (2-1.3)*50 = 35 gm.
permanent hardness therefore becomes = 35/200 * 1000 = 175 ppm.