What is the present worth of ₹660 due in 1 year at 10% per annum?

₹600. PW = 100 A100 + RT = 100 660110 = ₹600.

For ₹660 due in 1 year at 10% per annum, what is the true discount?

₹60. TD = A - PW = 660 - 600 = ₹60 — the simple interest on the present worth of ₹600 for 1 year at 10%.

What is the true discount on a bill of ₹1,860 due in 3 years at 8% per annum?

₹360. TD = A RT100 + RT = 1860 24124 = ₹360.

The present worth of a sum due in 2 years is ₹1,600 and the true discount is ₹160. What is the rate percent per annum?

5%. The true discount is the simple interest on the present worth: 160 = 1600 R 2100 = 32R, so R = 5\%.

The true discount on a sum due 6 months hence at 8% per annum is ₹40. What is the banker's gain?

₹1.60. PW = TD 100RT = 40 1004 = ₹1,000. Then BG = TD^2PW = 16001000 = ₹1.60.

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Quantitative Aptitude · Commercial Maths

True Discount — Questions & Answers

True discount is the difference between the amount due later and its present worth, where the present worth would earn exactly that much simple interest over the period.

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Key formulas

$\text{PW} = \dfrac{100 \times A}{100 + RT}$ ; $\;\text{TD} = A - \text{PW} = \dfrac{A \times RT}{100 + RT}$
$\text{TD} = \dfrac{\text{PW} \times R \times T}{100}$ (simple interest on the present worth)
$A = \dfrac{\text{TD}^2}{\text{BG}} + \text{TD}$ where BG is the banker's gain

5 solved True Discount questions

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01
What is the present worth of ₹660 due in 1 year at 10% per annum?
5 steps · reveal one at a time
1. Step 1: Understand the problem
  We need to find the Present Worth ( $PW$ ) of a future amount. We are given the future amount ( $A = \text{Rs}\,660$ ), the time period ( $T = 1$ year), and the annual interest rate ( $R = 10\%$ ).
2. Step 2: Recall the formula
  The formula to calculate the Present Worth ( $PW$ ) for a given future amount ( $A$ ) at a certain rate ( $R$ ) over a period ( $T$ ) is $PW = \dfrac{100 \times A}{100 + RT}$ .
3. Step 3: Substitute and calculate
  Now, substitute the given values into the formula: $PW = \dfrac{100 \times 660}{100 + 10 \times 1}$ . This simplifies to $PW = \dfrac{66000}{100 + 10} = \dfrac{66000}{110}$ .
4. Step 4: Perform the division
  Completing the calculation, $PW = \dfrac{66000}{110} = \text{Rs}\,600$ . This is the present worth of the amount due.
5. Step 5: The answer
  So the answer is (B) ₹600, because this is the calculated present worth based on the provided future amount, interest rate, and time.
02
For ₹660 due in 1 year at 10% per annum, what is the true discount?
5 steps · reveal one at a time
1. Step 1: Understand the Goal
  We need to find the True Discount (TD) for a bill. This is the difference between the face value of the bill (the amount due) and its present worth.
2. Step 2: Recall the Formula
  The amount due ( $A$ ) is the present worth ( $PW$ ) plus the interest on that present worth. So, $A = PW + \frac{PW \times R \times T}{100}$ . We can rearrange this to find $PW = \frac{A}{1 + \frac{R \times T}{100}}$ .
3. Step 3: Calculate Present Worth
  Given $A = \text{\text{Rs}\,}660$ , $R = 10\%$ , and $T = 1$ year. Substitute these values: $PW = \frac{660}{1 + \frac{10 \times 1}{100}} = \frac{660}{1 + 0.1} = \frac{660}{1.1} = \text{\text{Rs}\,}600$ .
4. Step 4: Find True Discount
  The True Discount is the difference between the Amount Due and the Present Worth. So, $TD = A - PW = \text{\text{Rs}\,}660 - \text{\text{Rs}\,}600 = \text{\text{Rs}\,}60$ . This is also the simple interest on the present worth.
5. Step 5: The answer
  So the answer is (C) ₹60. This value represents the interest earned on the present worth over the given period.
03
What is the true discount on a bill of ₹1,860 due in 3 years at 8% per annum?
5 steps · reveal one at a time
1. Step 1: Identify the Goal
  We need to find the true discount (TD) on a bill. The bill's face value (amount) is $\text{Rs}\,1,860$ , it's due in 3 years, and the interest rate is 8% per annum.
2. Step 2: Recall the Formula
  The formula for true discount (TD) is $TD = \frac{A \times RT}{100 + RT}$ , where $A$ is the amount, $R$ is the rate of interest, and $T$ is the time in years.
3. Step 3: Calculate RT Value
  First, let's calculate the product of the rate and time, $RT$ . Given $R = 8\%$ and $T = 3$ years, we have $RT = 8 \times 3 = 24$ .
4. Step 4: Apply the Formula
  Now, substitute the values into the formula: $A = 1860$ and $RT = 24$ . So, $TD = \frac{1860 \times 24}{100 + 24} = \frac{1860 \times 24}{124}$ .
5. Step 5: The answer
  So the answer is (A) ₹360. Calculating the expression gives $TD = \frac{44640}{124} = 360$ . Thus, the true discount is $\text{Rs}\,360$ .
04
The present worth of a sum due in 2 years is ₹1,600 and the true discount is ₹160. What is the rate percent per annum?
5 steps · reveal one at a time
1. Step 1: Recall True Discount
  The true discount is the simple interest calculated on the present worth of a sum. It's the difference between the sum due and its present worth.
2. Step 2: List the values
  We are given the present worth ( $PW = \text{\text{Rs}\,}1,600$ ), the time period ( $T = 2$ years), and the true discount ( $TD = \text{\text{Rs}\,}160$ ). We need to find the rate percent per annum ( $R$ ).
3. Step 3: Apply the formula
  The formula for true discount is $TD = \dfrac{PW \times R \times T}{100}$ . Let's substitute the given values into this formula to solve for $R$ .
4. Step 4: Calculate the rate
  Substituting the values, we get $160 = \dfrac{1600 \times R \times 2}{100}$ . This simplifies to $160 = 32R$ . To find $R$ , divide $160$ by $32$ , which gives $R = 5\%$ .
5. Step 5: The answer
  So the answer is (B) 5%. The rate percent per annum is 5%, as calculated from the true discount formula.
05
The true discount on a sum due 6 months hence at 8% per annum is ₹40. What is the banker's gain?
4 steps · reveal one at a time
1. Step 1: Identify known values
  We are given the True Discount (TD) as ₹40. The time is 6 months, which is $0.5$ years, and the rate is $8\%$ per annum. We need to find the Banker's Gain (BG).
2. Step 2: Calculate Present Worth
  First, find the Present Worth (PW) using the formula $PW = \dfrac{TD \times 100}{RT}$ . Here, $R = 8$ and $T = 0.5$ , so $RT = 8 \times 0.5 = 4$ . Plugging in the values, $PW = \dfrac{40 \times 100}{4} = \dfrac{4000}{4} = \text{Rs}\,1,000$ .
3. Step 3: Find Banker's Gain
  Now we can calculate the Banker's Gain (BG). The formula for Banker's Gain is $BG = \dfrac{TD^2}{PW}$ . We know $TD = 40$ and $PW = 1,000$ . So, $BG = \dfrac{40^2}{1000} = \dfrac{1600}{1000} = \text{Rs}\,1.60$ .
4. Step 4: The answer
  So the answer is (D) ₹1.60. This is the value obtained for the Banker's Gain after calculating the Present Worth.

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