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).
Aptitude
Banker's Discount
Difficulty: Medium
Choose an option
-
A11%
-
B10%
-
C5%
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D51/3
Answer
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.
Final Answer:5%