Find TD and BG from given BD: The banker’s discount on ₹1650 due a certain time hence is ₹165. Determine the true discount and the banker’s gain.

Difficulty: Easy

Correct Answer: Rs. 150, Rs. 15

Explanation:

Introduction / Context:
Knowing BD on a face amount directly gives r t because BD = A * r * t. Once r t is known, TD and BG follow immediately.

Given Data / Assumptions:

Concept / Approach:

BD = A * r * t ⇒ r t = BD / A = 165 / 1650 = 0.10 TD = A * (r t) / (1 + r t) BG = BD − TD

Step-by-Step Solution:

TD = 1650 * 0.10 / 1.10 = ₹150 BG = 165 − 150 = ₹15

Verification / Alternative check:
PW = A − TD = 1650 − 150 = ₹1500; interest on PW at r t = 0.10 equals ₹150 (the TD), confirming consistency.

Why Other Options Are Wrong:
They do not reflect r t = 0.10 implied by BD/A = 0.10.

Common Pitfalls:
Confusing TD with BD or computing TD without dividing by (1 + r t).

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