A local tyre distributor expects to sell approximately 9600 steel belted radial tyres next year. Annual carrying cost is Rs. 16 per tyre and ordering cost is Rs. 75. The economic order quantity of the tyres is

The correct option is 300.

Economic Order Quantity (EOQ) is the optimal order quantity that minimizes the total inventory costs, which include ordering costs and holding (carrying) costs.

The formula for Economic Order Quantity is given by:

$\mathrm{EOQ}=\sqrt{\frac{2\times D\times S}{H}}$

Where:
- $D$ is the annual demand = 9600 tyres
- $S$ is the ordering cost per order = Rs. 75
- $H$ is the annual carrying cost per tyre = Rs. 16

Substituting the given values into the formula:

$\mathrm{EOQ}=\sqrt{\frac{2\times 9600\times 75}{16}}$

First, calculate the numerator:

$2\times 9600\times 75=1440000$

Next, divide by the annual carrying cost ($H$):

$\frac{1440000}{16}=90000$

Finally, take the square root of the result to find the EOQ:

$\mathrm{EOQ}=\sqrt{90000}=300$

Therefore, the economic order quantity of the tyres is 300.