The banker's discount on a certain sum due 2 years hence is $\frac{11}{10}$ of the true discount. The rate percent is

### Concept & Formula The difference between the Banker's Discount (B.D.) and the True Discount (T.D.) is the Banker's Gain (B.G.). The Banker's Gain is defined mathematically as the simple interest calculated on the True Discount. $$B.G. = B.D. - T.D.$$ $$B.G. = \frac{T.D. \times R \times T}{100}$$ ### Step-by-Step Solution 1. **Given:** $B.D. = \frac{11}{10} T.D.$, Time ($T$) = 2 years. 2. **Calculate Banker's Gain (B.G.) in terms of T.D.:** $B.G. = B.D. - T.D.$ $B.G. = \frac{11}{10} T.D. - T.D. = \frac{1}{10} T.D.$ 3. **Equate and solve for Rate ($R$):** Using $B.G. = \frac{T.D. \times R \times T}{100}$ $\frac{1}{10} T.D. = \frac{T.D. \times R \times 2}{100}$ Cancel T.D. from both sides: $\frac{1}{10} = \frac{2R}{100}$ $\frac{1}{10} = \frac{R}{50}$ $R = \frac{50}{10} = 5\%$ ### Exam Strategy & Shortcut Whenever a ratio is given like $B.D. = \frac{11}{10} T.D.$, it implies that for every 10 units of T.D., there is 1 extra unit of interest (the B.G.). So, interest on 10 units for 2 years is 1 unit. Rate $R = \frac{\text{Interest} \times 100}{\text{Principal} \times \text{Time}} = \frac{1 \times 100}{10 \times 2} = \frac{100}{20} = 5\%$. This ratio-based approach is extremely fast. ### Common Pitfall A common pitfall is plugging in $\frac{11}{10}$ directly into rate formulas without finding the difference (Banker's Gain) first. The fraction $\frac{11}{10}$ represents the total amount multiplier, not the interest portion. ### Final Answer Therefore, the correct answer is **5%**.