The present worth of a bill due sometime hence is Rs 1100 and the true discount on the bill is Rs 110. What is the banker's discount on the bill (in rupees)?

Introduction / Context:
This question provides the present worth and the true discount of a bill and asks for the banker's discount. True discount is the difference between the face value and the present worth. Banker's discount is calculated on the face value at the same rate and time. Using the relationship between these quantities, we can determine the face value and then compute the banker's discount without needing the rate or time explicitly.

Given Data / Assumptions:
- Present worth PW = Rs 1100
- True discount TD = Rs 110
- Face value F of the bill is PW + TD
- Banker's discount BD is to be found at the same rate and time as TD
- The interest is simple throughout.

Concept / Approach:
By definition TD = F − PW, so F = PW + TD. For the same rate and time, the discount is proportional to the principal on which it is calculated. True discount is interest on present worth, while banker's discount is interest on face value. Therefore BD / TD = F / PW. Having PW and TD, we first compute F, then use this ratio to find BD directly from TD.

Step-by-Step Solution:
Step 1: Compute the face value of the bill: F = PW + TD = 1100 + 110 = Rs 1210.Step 2: For the same rate and time, BD and TD are proportional to the amounts on which they are calculated.Step 3: Hence BD / TD = F / PW.Step 4: Substitute values: BD / 110 = 1210 / 1100.Step 5: Simplify the fraction 1210 / 1100 to 11 / 10.Step 6: Therefore BD = 110 × 11 / 10 = 11 × 11 = Rs 121.

Verification / Alternative check:
We can reinterpret the ratio F / PW = 11 / 10 as indicating that the face value is 10 percent more than the present worth. This means the true discount corresponds to 10 percent of PW. If TD is 110, 10 percent of PW is 110, so PW is 1100, which is consistent. Banker's discount must then correspond to the same percentage applied to the face value, giving 10 percent of 1210 which is 121. This confirms that BD = 121 is logically correct.

Why Other Options Are Wrong:
An amount like 112 or 130 does not match the exact 11 to 10 ratio between face value and present worth. The value 145 or 136 would suggest a larger percentage discount on the face value than is implied by the relation between PW and TD. Only Rs 121 preserves the correct proportional relationship between true discount and banker's discount at the same rate and time.

Common Pitfalls:
Students sometimes calculate BD as TD plus some guessed banker's gain instead of using the proportional reasoning. Others forget that TD is based on present worth, not on face value, which leads to incorrect expressions. Keeping the simple identity BD / TD = F / PW in mind provides a clean and reliable way to answer such questions.

Final Answer:
The banker's discount on the bill is Rs. 121.