For a sum due 2 years later, the banker’s discount (BD) is 11/10 of the true discount (TD). Find the annual rate percent (simple interest).

Difficulty: Medium

11%
10%
5%
51/3

Correct Answer: 5%

Explanation:

Introduction / Context:
Relating BD and TD via their ratio immediately gives x = r * t, because BD/TD = 1 + x. With time known, we solve for r directly. This avoids needing monetary amounts.

Given Data / Assumptions:

BD = (11/10) * TD.
t = 2 years.

Concept / Approach:
From BD/TD = 1 + x, we have 11/10 = 1 + x ⇒ x = 1/10 = 0.1. Since x = r * t, r = x / t = 0.1 / 2.

Step-by-Step Solution:

1 + x = 11/10 ⇒ x = 1/10.t = 2 ⇒ r = x / t = (1/10) / 2 = 1/20 = 0.05 = 5% p.a.

Verification / Alternative check:
Check: BD/TD should be 1 + x = 1.1 = 11/10, matches the condition.

Why Other Options Are Wrong:
10% and 11% imply x = 0.2 or 0.22 over 2 years, not consistent with BD/TD = 11/10. “51/3” is not a valid percent value here.

Common Pitfalls:
Forgetting BD/TD = 1 + x or dividing by years incorrectly when computing r.

For a sum due 2 years later, the banker’s discount (BD) is 11/10 of the true discount (TD). Find the annual rate percent (simple interest).

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