Rate from BD and TD (repeat form): The banker’s discount on a sum for 1.5 years is ₹60 and the true discount on the same sum for 2 years is ₹75. Find the rate percent.

Difficulty: Medium

5%
6%
62/3%
31/3%
None of these

Correct Answer: 31/3%

Explanation:

Introduction / Context:
This is the same structural setup as a prior item and leads to the same rate. We repeat the concise derivation for completeness and clarity.

Given Data / Assumptions:
BD(1.5 y) = ₹60, TD(2 y) = ₹75, face value A common, rate r unknown.

Concept / Approach:

BD = A * r * 1.5 ⇒ A r = 40 TD = A * (2r) / (1 + 2r) = 75 ⇒ A(2r) = 80 75 = 80 / (1 + 2r) ⇒ 1 + 2r = 16/15 ⇒ r = 1/30 = 3 1/3 %

Final Answer:
31/3%

← Previous Question Next Question→

More Questions from Banker's Discount

Difference between BD and TD for a short term: Find the difference between the banker’s discount and the true discount on ₹8100 for 3 months at 5% per annum.
Find the face value from interest and discount on the same sum: The simple interest on a certain sum is ₹67.20 and the (true) discount on the same sum for the same time and rate is ₹60. Find the sum (face value).
Find the face value from banker’s gain: The banker’s gain on a bill due 1 year 4 months hence at 7.5% per annum (simple interest) is ₹16. Find the face value of the bill.
Find true discount from banker’s gain: The banker’s gain on a bill due 1 year hence at 10% per annum is ₹20. What is the true discount?
Find banker’s discount from banker’s gain: The banker’s gain on a sum due 3 years hence at 12% per annum is ₹360. Compute the banker’s discount.
Find the rate percent from true discount and term: The true discount on ₹2562 due 4 months hence is ₹122. Determine the annual simple interest rate.
Present worth and true discount (simple interest): A sum of Rs 9300 is due exactly 3 years from now at a simple interest rate of 8% per annum. Compute the present worth (i.e., the amount which, if invested today at 8% simple interest, will grow to Rs 9300 in 3 years). Also find the true discount (difference between the sum due and its present worth). Finally, which of the following values equals the true discount?
Present worth of two equal half-yearly instalments: A total of Rs 702 is to be paid in two equal instalments due at the end of 6 months and 12 months respectively. If interest is 8% per annum (simple interest), find the present worth today of the two instalments combined.
From PW and true discount, find banker’s discount and banker’s gain: The present worth (PW) of a bill due sometime hence is Rs 1600, and its true discount (TD) is Rs 160. Find the banker’s discount (BD) and the extra gain (banker’s gain, BG).
Find the discount date from the rebate received: A bill for Rs 17,850 is nominally due on 21 May 1991. Its holder receives Rs 357 less than the amount of the bill by discounting it at 5% per annum (banker’s discount). On which date was the bill discounted? (Assume 3 days of grace.)

Discussion & Comments

No comments yet. Be the first to comment!

Join Discussion