The banker's discount on a certain sum due 2 years hence is 11/10 of the true discount. If the transaction is at simple interest, what is the annual rate of interest (rate percent)?

Introduction:
This question compares the banker's discount with the true discount for the same sum of money and the same time period. By using the standard relationship between banker's discount and true discount, we can find the rate of interest per annum.

Given Data / Assumptions:
Time t = 2 years. Banker's discount (BD) = (11/10) * true discount (TD). Simple interest is used. We must find the rate of interest r (in percent per annum).

Concept / Approach:
For a sum with face value P: BD = P * r * t / 100. TD = P * r * t / (100 + r * t). Therefore, BD / TD = (100 + r * t) / 100. We are given BD = (11/10) * TD, so BD / TD = 11/10. We equate these expressions and solve for r * t, then obtain r since t is known.

Step-by-Step Solution:
Step 1: Set up the ratio. BD / TD = (100 + r * t) / 100 = 11 / 10. Step 2: Cross-multiply to find r * t. 100 + r * t = 100 * (11 / 10) = 110. r * t = 110 − 100 = 10. Step 3: Time t = 2 years, so r * 2 = 10 ⇒ r = 10 / 2 = 5% per annum.

Verification / Alternative check:
If r = 5%, t = 2 years, then r * t = 10. The ratio BD / TD should be: (100 + 10) / 100 = 110 / 100 = 11 / 10, which exactly matches the condition BD = (11/10) * TD.

Why Other Options Are Wrong:
10%: Would give r * t = 20, leading to BD / TD = 120 / 100 = 6/5, not 11/10. 7%: Gives r * t = 14, so BD / TD = 114 / 100 = 57/50, not 11/10. 8%: Leads to r * t = 16 and BD / TD = 116 / 100. 6%: Leads to r * t = 12 and BD / TD = 112 / 100.

Common Pitfalls:
A common mistake is to treat BD and TD as if they were both simple interest on the present worth, or to forget the exact BD / TD ratio formula. Always derive the relationship using the standard formulas for BD and TD before solving for the rate.

Final Answer:
The annual rate of interest is 5% per annum.