Purchase Price Calculation:

To calculate the purchase price of the firm, we need to consider the equity share, debentures, and the balance amount.

Equity Share:
The company agreed to pay 70% of the amount in equity shares. The face value of each equity share is Rs 10 with a 10% premium.

Let's calculate the number of equity shares issued:
Face Value of Equity Share = Rs 10
Premium on Equity Share = 10% of Rs 10 = Rs 1
Total Cost per Equity Share = Face Value + Premium = Rs 10 + Rs 1 = Rs 11

Amount paid in equity shares = 70% of the purchase price
Let the purchase price be P.
Equity Share Amount = 0.70P

Number of equity shares issued = Equity Share Amount / Total Cost per Equity Share
Let the number of equity shares be x.
Equity Share Amount = Number of Equity Shares * Total Cost per Equity Share
0.70P = x * Rs 11

Debentures:
The company agreed to pay 25% of the amount in debentures. The face value of each debenture is Rs 100.

Amount paid in debentures = 25% of the purchase price
Debenture Amount = 0.25P

Number of debentures issued = Debenture Amount / Face Value of Debenture
Let the number of debentures be y.
Debenture Amount = Number of Debentures * Face Value of Debenture
0.25P = y * Rs 100

Balance Amount:
The remaining balance amount is given as Rs 165,000.

Equity Share Amount + Debenture Amount + Balance Amount = Purchase Price
0.70P + 0.25P + Rs 165,000 = P

To find the value of P, we can solve the above equation.

Summary:
The purchase price of the firm can be calculated by considering the amount paid in equity shares, debentures, and the balance amount. The equity share amount is calculated by multiplying the number of equity shares with the total cost per equity share. The debenture amount is calculated by multiplying the number of debentures with the face value of each debenture. Finally, the purchase price is obtained by summing up the equity share amount, debenture amount, and the balance amount.