The following journal entry appears in the books of X Co. Ltd.

Bank A/c Dr. 4,75,000

Loss on issue of debenture A/c 75,000

To 12% Debentures A/c Dr. 5,00,000

To Premium on Redemption of Debenture A/с 50,000

In this case the debentures have been issued at a discount of 5%. What is the rate of premium on redemption of debentures ?

The correct option is 10%.

Let us break down the journal entry step-by-step to understand the calculation of the rate of premium on redemption of debentures.

From the journal entry, we have the following values:
1. Face value of Debentures (credited to 12% Debentures A/c) = Rs 5,00,000
2. Amount received in Bank (Bank A/c Dr.) = Rs 4,75,000
3. Premium on Redemption of Debentures (credited to Premium on Redemption of Debenture A/c) = Rs 50,000
4. Total Loss on Issue of Debentures = Rs 75,000

First, let's verify the discount on issue of debentures. The problem states that the debentures have been issued at a discount of 5%.
Discount on issue = 5% of Face Value
Discount on issue = $\frac{5}{100}\times \mathrm{5,00,000}=\mathrm{25,000}$
This matches the entry, since the bank received Rs 4,75,000 (which is Rs 5,00,000 minus the Rs 25,000 discount).

Next, we know that the "Loss on Issue of Debentures A/c" comprises two elements:
Total Loss on Issue = Discount on Issue + Premium on Redemption
Total Loss on Issue = Rs 25,000 + Rs 50,000 = Rs 75,000, which matches the journal entry.

Now, we calculate the rate of premium on redemption. The premium on redemption is calculated as a percentage of the nominal (face) value of the debentures:
Rate of Premium on Redemption = $\left(\frac{\text{Premium on Redemption}}{\text{Face Value of Debentures}}\right)\times 100$

Substituting the values into the formula:
Rate of Premium on Redemption = $\left(\frac{\mathrm{50,000}}{\mathrm{5,00,000}}\right)\times 100$

Rate of Premium on Redemption = $0.10\times 100=10\%$

Thus, the rate of premium on redemption of debentures is 10%.