What is the banker's discount on ₹1,800 due in 8 months at 12% per annum?

₹144. The banker's discount is the simple interest on the face value: 1800 12 812100 = ₹144.

The banker's discount on a bill is ₹80 and the true discount is ₹75. What is the banker's gain?

₹5. BG = BD - TD = 80 - 75 = ₹5.

The banker's gain on a bill due 2 years hence at 5% per annum is ₹8. What is the true discount?

₹80. BG = TD R T100, so 8 = TD 10100, giving TD = ₹80.

If the true discount on a sum is ₹20 and the banker's discount is ₹24, what is the face value of the bill?

₹120. A = TD BDBD - TD = 20 244 = ₹120.

The banker's discount on a sum due 4 years hence at 10% per annum is ₹420. What is the true discount?

₹300. TD = BD 100100 + RT = 420 100100 + 40 = ₹300.

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Quantitative Aptitude · Commercial Maths

Banker's Discount — Questions & Answers

Banker's discount is the simple interest on the full face value of a bill for the unexpired time. Banker's gain is the small extra it charges over the true discount.

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Key formulas included

Key formulas

$\text{BD} = \dfrac{A \times R \times T}{100}$ (simple interest on the face value $A$ )
$\text{BG} = \text{BD} - \text{TD} = \dfrac{\text{TD} \times R \times T}{100} = \dfrac{\text{TD}^2}{\text{PW}}$
$\text{BD} = \dfrac{\text{TD} \times A}{\text{PW}}$

5 solved Banker's Discount questions

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01
What is the banker's discount on ₹1,800 due in 8 months at 12% per annum?
5 steps · reveal one at a time
1. Step 1: Understand Banker's Discount
  The Banker's Discount (BD) is the simple interest calculated on the face value (or sum due) of a bill for the unexpired period. It's like charging interest upfront.
2. Step 2: Identify Given Values
  We are given the face value $P = \text{Rs}\,1,800$ . The annual rate of interest is $R = 12\%$ . The time period is $T = 8$ months.
3. Step 3: Convert Time and Formula
  First, convert the time to years: $T = \frac{8}{12}$ years. The formula for Banker's Discount is $BD = \frac{P \times R \times T}{100}$ .
4. Step 4: Calculate the Discount
  Substitute the values into the formula: $BD = \frac{1800 \times 12 \times \frac{8}{12}}{100}$ . This simplifies to $BD = \frac{1800 \times 12 \times 8}{12 \times 100}$ .
5. Step 5: The answer
  So the answer is (B) ₹144. Performing the calculation gives $BD = \frac{1800 \times 8}{100} = 18 \times 8 = \text{Rs}\,144$ . This matches option (B).
02
The banker's discount on a bill is ₹80 and the true discount is ₹75. What is the banker's gain?
4 steps · reveal one at a time
1. Step 1: Identify Given Values
  We are given the banker's discount ( $BD$ ) as ₹80 and the true discount ( $TD$ ) as ₹75. Our goal is to find the banker's gain.
2. Step 2: Recall the Formula
  The banker's gain ( $BG$ ) is defined as the difference between the banker's discount and the true discount. The formula is $BG = BD - TD$ .
3. Step 3: Calculate Banker's Gain
  Now, substitute the given values into the formula: $BG = 80 - 75$ . Performing the subtraction gives $BG = 5$ . So, the banker's gain is ₹5.
4. Step 4: The answer
  So the answer is (B) ₹5. This value is obtained by directly applying the formula for banker's gain, which is the banker's discount minus the true discount.
03
The banker's gain on a bill due 2 years hence at 5% per annum is ₹8. What is the true discount?
4 steps · reveal one at a time
1. Step 1: Identify knowns
  We are given the Banker's Gain (BG) as ₹8. The time (T) is 2 years, and the rate (R) is 5% per annum. Our goal is to find the True Discount (TD).
2. Step 2: Recall formula
  The relationship between Banker's Gain (BG), True Discount (TD), Rate (R), and Time (T) is given by the formula: $BG = \frac{TD \times R \times T}{100}$ .
3. Step 3: Substitute and solve
  Substitute the known values into the formula: $8 = \frac{TD \times 5 \times 2}{100}$ . This simplifies to $8 = \frac{TD \times 10}{100}$ . Now, solve for TD: $TD = \frac{8 \times 100}{10} = 8 \times 10 = 80$ .
4. Step 4: The answer
  So the answer is (C) ₹80, because the true discount is calculated to be ₹80 based on the given banker's gain, rate, and time.
04
If the true discount on a sum is ₹20 and the banker's discount is ₹24, what is the face value of the bill?
4 steps · reveal one at a time
1. Step 1: Identify Given Values
  We are given the true discount (TD) on a sum, which is $\text{Rs}\,20$ . We also know the banker's discount (BD), which is $\text{Rs}\,24$ . Our goal is to find the face value of the bill.
2. Step 2: Recall the Formula
  The relationship between true discount, banker's discount, and the face value of the bill (let's call it $A$ ) is given by a specific formula. The formula is: $A = \frac{TD \times BD}{BD - TD}$ .
3. Step 3: Calculate Face Value
  Now, substitute the given values into the formula. We have $TD = 20$ and $BD = 24$ . So, $A = \frac{20 \times 24}{24 - 20}$ . This simplifies to $A = \frac{480}{4}$ , which gives $A = 120$ .
4. Step 4: The answer
  So the answer is (C) ₹120. The face value of the bill is calculated by using the formula that relates the true discount, banker's discount, and the face value.
05
The banker's discount on a sum due 4 years hence at 10% per annum is ₹420. What is the true discount?
5 steps · reveal one at a time
1. Step 1: Identify Given Values
  We are given the Banker's Discount ( $BD$ ) as ₹420. The time ( $T$ ) is 4 years, and the rate ( $R$ ) is 10% per annum. Our goal is to find the True Discount ( $TD$ ). This is a common problem in commercial arithmetic.
2. Step 2: Recall the Formula
  The relationship between Banker's Discount ( $BD$ ) and True Discount ( $TD$ ) is given by a specific formula. It connects these values with the rate ( $R$ ) and time ( $T$ ): $TD = \dfrac{BD \times 100}{100 + RT}$ .
3. Step 3: Substitute and Calculate
  Now, let's substitute the given values into the formula. We have $BD = 420$ , $R = 10$ , and $T = 4$ . First, calculate $RT = 10 \times 4 = 40$ . Then, plug these into the formula: $TD = \dfrac{420 \times 100}{100 + 40}$ .
4. Step 4: Simplify to Find TD
  Continue simplifying the expression: $TD = \dfrac{420 \times 100}{140}$ . This simplifies to $TD = \dfrac{42000}{140}$ . Performing the division, we get $TD = 300$ . So, the true discount is ₹300.
5. Step 5: The answer
  So the answer is (B) ₹300. This value represents the true discount on the sum, calculated using the given banker's discount, rate, and time.

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