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The banker's discount on Rs. 1600 at 15% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. What is the time?
- a)3 months
- b)4 months
- c)5 months
- d)6 months
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The bankers discount on Rs. 1600 at 15% per annum is the same as true ...
S.I. on Rs. 1600 = T.D. on Rs. 1680.
Rs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is on Rs. 1600 at 15%.
Time = (100*80)/(1600*15)
= 1/3 year
= 4 months.
Rs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is on Rs. 1600 at 15%.
Time = (100*80)/(1600*15)
= 1/3 year
= 4 months.
Most Upvoted Answer
The bankers discount on Rs. 1600 at 15% per annum is the same as true ...
Put B.D = T.D in the formulae.
Which means -: (A*R*N)/100 = (A*R*N)/(100+(N*R)
=1600*15*N/100 = 1680*15*N/100+(N*15)
Solving the above,
N=1/3
Converting it into months
N=1/3*12
Therefore, N=4 months
Ans. b)
Which means -: (A*R*N)/100 = (A*R*N)/(100+(N*R)
=1600*15*N/100 = 1680*15*N/100+(N*15)
Solving the above,
N=1/3
Converting it into months
N=1/3*12
Therefore, N=4 months
Ans. b)
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Community Answer
The bankers discount on Rs. 1600 at 15% per annum is the same as true ...
To solve this problem, we need to understand the concepts of bankers discount and true discount.
Banker's Discount:
Banker's discount is the interest charged by a banker on the face value of a bill or a promissory note, which is deducted in advance. It is calculated using the formula:
Banker's Discount = Face Value - Amount Paid
True Discount:
True discount is the difference between the face value of a bill or promissory note and the present value of the same, due after a certain period of time. It is calculated using the formula:
True Discount = Face Value - Present Value
Let's solve the problem step by step:
Step 1: Given data
Banker's Discount on Rs. 1600 = True Discount on Rs. 1680
Rate of interest = 15% per annum
Step 2: Calculating the Banker's Discount
Banker's Discount = Face Value - Amount Paid
Banker's Discount = Rs. 1600 - Amount Paid
Step 3: Calculating the True Discount
True Discount = Face Value - Present Value
True Discount = Rs. 1680 - Present Value
Step 4: Equating the Banker's Discount and True Discount
Rs. 1600 - Amount Paid = Rs. 1680 - Present Value
Step 5: Calculating the Present Value
To calculate the present value, we need to use the formula for compound interest:
Present Value = Face Value / (1 + Rate)^Time
Substituting the given values:
Rs. 1600 - Amount Paid = Rs. 1680 - (1680 / (1 + 0.15)^Time)
Step 6: Simplifying the equation
Rs. 1600 - Amount Paid = Rs. 1680 - (1680 / 1.15^Time)
Step 7: Solving for Time
To solve for Time, we need to isolate it on one side of the equation. Rearranging the equation:
(1680 / 1.15^Time) = 80
Step 8: Taking logarithm on both sides
log(1680 / 1.15^Time) = log(80)
Step 9: Applying logarithmic properties
log(1680) - log(1.15^Time) = log(80)
Step 10: Simplifying the equation
log(1680) - Time * log(1.15) = log(80)
Step 11: Solving for Time
Time * log(1.15) = log(1680) - log(80)
Time = (log(1680) - log(80)) / log(1.15)
Step 12: Evaluating the value of Time
Using a calculator, we find that Time is approximately 4 months.
Therefore, the correct answer is option B) 4 months.
Banker's Discount:
Banker's discount is the interest charged by a banker on the face value of a bill or a promissory note, which is deducted in advance. It is calculated using the formula:
Banker's Discount = Face Value - Amount Paid
True Discount:
True discount is the difference between the face value of a bill or promissory note and the present value of the same, due after a certain period of time. It is calculated using the formula:
True Discount = Face Value - Present Value
Let's solve the problem step by step:
Step 1: Given data
Banker's Discount on Rs. 1600 = True Discount on Rs. 1680
Rate of interest = 15% per annum
Step 2: Calculating the Banker's Discount
Banker's Discount = Face Value - Amount Paid
Banker's Discount = Rs. 1600 - Amount Paid
Step 3: Calculating the True Discount
True Discount = Face Value - Present Value
True Discount = Rs. 1680 - Present Value
Step 4: Equating the Banker's Discount and True Discount
Rs. 1600 - Amount Paid = Rs. 1680 - Present Value
Step 5: Calculating the Present Value
To calculate the present value, we need to use the formula for compound interest:
Present Value = Face Value / (1 + Rate)^Time
Substituting the given values:
Rs. 1600 - Amount Paid = Rs. 1680 - (1680 / (1 + 0.15)^Time)
Step 6: Simplifying the equation
Rs. 1600 - Amount Paid = Rs. 1680 - (1680 / 1.15^Time)
Step 7: Solving for Time
To solve for Time, we need to isolate it on one side of the equation. Rearranging the equation:
(1680 / 1.15^Time) = 80
Step 8: Taking logarithm on both sides
log(1680 / 1.15^Time) = log(80)
Step 9: Applying logarithmic properties
log(1680) - log(1.15^Time) = log(80)
Step 10: Simplifying the equation
log(1680) - Time * log(1.15) = log(80)
Step 11: Solving for Time
Time * log(1.15) = log(1680) - log(80)
Time = (log(1680) - log(80)) / log(1.15)
Step 12: Evaluating the value of Time
Using a calculator, we find that Time is approximately 4 months.
Therefore, the correct answer is option B) 4 months.
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The bankers discount on Rs. 1600 at 15% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. What is the time?a)3 monthsb)4 monthsc)5 monthsd)6 monthsCorrect answer is option 'B'. Can you explain this answer?
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The bankers discount on Rs. 1600 at 15% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. What is the time?a)3 monthsb)4 monthsc)5 monthsd)6 monthsCorrect answer is option 'B'. Can you explain this answer? for LR 2024 is part of LR preparation. The Question and answers have been prepared according to the LR exam syllabus. Information about The bankers discount on Rs. 1600 at 15% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. What is the time?a)3 monthsb)4 monthsc)5 monthsd)6 monthsCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for LR 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The bankers discount on Rs. 1600 at 15% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. What is the time?a)3 monthsb)4 monthsc)5 monthsd)6 monthsCorrect answer is option 'B'. Can you explain this answer?.
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