Q.For $\sum p_0q_0=1974$, $\sum p_1q_0=3140$, $\sum p_1q_1=2005$ find the Cost of Living Index by Aggregate Expenditure Method.

Fisher's ideal index number uniquely satisfies both the Time Reversal and Factor Reversal tests, hence it is called ideal; option (b).

Why Fisher's. Fisher's index is the geometric mean of Laspeyres' and Paasche's indices:

$P_{01}^{F}=\sqrt{P_{01}^{L}\times P_{01}^{P}}.$

• Time Reversal test: $P_{01}\times P_{10}=1$ — satisfied by Fisher's. …

Fisher's ideal index combines Laspeyre's and Paasche's indices as their geometric mean.

Fisher's ideal price index number is defined as

$P_{01}^{F}=\sqrt{P_{01}^{L}\times P_{01}^{P}}=\sqrt{\frac{\sum p_1q_0}{\sum p_0q_0}\times\frac{\sum p_1q_1}{\sum p_0q_1}}\times 100,$ …