What is the population of State A ?
A. After an increase in the population of state A by 15% it becomes 1.6 lakhs
B. Ratio of population of state A to that of state B is 7 : 8.
C. Population of state B is 1.6 lakhs.

I : Let population before increase = x lakhs

$$\frac{1.6-x}{x}$$*100 = 15

=> x=1.39 = ~1.4 lakhs

Thus, I is sufficient.

II : Ratio of population of state A to state B = 7:8

Thus, we cannot find population of state A. II is not sufficient alone.

III : Population of B = 1.6 lakhs. Population of A is not given.

Thus, III is not suficient alone.

II & III : Let population of A = 7x

Population of B = 8x = 1.6 lakhs => x = 0.2 lakhs

Thus, population of A = 7*0.2 = 1.4 lakhs.

Thus, II & III together are sufficient.