Calculation of Paasche's index number

Bowley's index number is given as 150, Fisher's index number is given as 149.95. We need to find out Paasche's index number.

Paasche's index number formula is given as:

Paasche's index number = (Current period quantity * Current period price) / (Base period quantity * Base period price)

To calculate Paasche's index number, we need to have the current period and base period quantities and their corresponding prices.

Since we are not given the quantities, we assume them to be 1.

Let the current period price be P1 and the base period price be P0.

Paasche's index number formula can be simplified as:

Paasche's index number = P1 / P0

We are given that Fisher's index number is 149.95.

Fisher's index number formula is given as:

Fisher's index number = √(Paasche's index number * Laspeyre's index number)

We know Fisher's index number and Laspeyre's index number is always less than Paasche's index number. Therefore, we can calculate the value of Paasche's index number using Fisher's index number.

Squaring both sides of Fisher's index number formula, we get:

Paasche's index number * Laspeyre's index number = Fisher's index number^2

Since Laspeyre's index number is less than Paasche's index number, we can assume it to be equal to 149.95.

Substituting the values in the above formula, we get:

Paasche's index number = Fisher's index number^2 / Laspeyre's index number = (149.95)^2 / 149.95 = 158

Therefore, the correct answer is option (a) 158.