Banker’s Discountबैंकर बट्टाquestions and answersप्रश्न और उत्तर
When a business sells a bill to a bank before it falls due, the bank pays less than the face value. The bank’s deduction is the banker’s discount, and it is a little more than the fair (true) discount. That extra is the banker’s gain.
Unlimitedअसीमितfresh questionsनए प्रश्न
Answersउत्तरalways one tap awayहमेशा एक टैप दूर
1subtopicउप-टॉपिक
Practice questions are in English for now.अभ्यास के प्रश्न अभी अंग्रेज़ी में हैं।
How banker’s discount worksबैंकर बट्टा को समझिए
The bank charges simple interest on the full face value of the bill for the time left: BD = A × R × T/100. The true discount on the same bill is only interest on the present worth, A × RT/(100 + RT), so BD is always larger.
Banker’s gain BG = BD − TD. It equals the simple interest on the true discount for the same time and rate, so BG = TD × R × T/100. From this, BD/TD = (100 + RT)/100.
Because BD is interest on A and BG is interest on TD at the same rate and time, A/TD = BD/BG. That gives the face value directly: A = BD × TD/(BD − TD).
Each trick says when to use it, why it works and when it fails. Formula tricks are checked by code over their whole range.हर ट्रिक बताती है कि उसे कब इस्तेमाल करें, वह क्यों काम करती है और कब नहीं। सूत्र वाली ट्रिक्स को कोड से उनकी पूरी रेंज पर जाँचा गया है।
Formulaसूत्र✓ Checked on 1,710 cases✓ 1,710 मामलों पर जाँची गई
Face value = BD × TD/(BD − TD)
Use it when:कब इस्तेमाल करें: You are given the banker’s discount and the true discount on the same bill and asked for its face value (or need BG).
Banker’s gain BG = BD − TD.
Face value A = BD × TD/BG.
Exampleउदाहरण
BD = ₹1,344 and TD = ₹1,200 on a bill. Face value?
→ 1,344 × 1,200/144 = ₹11,200
Why it works, and when it failsयह क्यों काम करती है, और कब नहीं
Why:क्यों: BD is the interest on A and BG = BD − TD is the interest on TD, at the same rate and time. Interest is proportional to the principal, so A/TD = BD/BG, giving A = BD × TD/(BD − TD).
Limits:सीमाएँ: BD and TD must be for the same bill, rate and time, under simple interest.
Mental mathsमानसिक गणित✓ Checked on 2,320 cases✓ 2,320 मामलों पर जाँची गई
BD ÷ TD = 1 + RT/100: read the rate off two discounts
Use it when:कब इस्तेमाल करें: BD and TD are both given (or BD and BG) and the rate or the time is unknown.
Divide BD by TD.
Subtract 1 and multiply by 100 to get R × T.
Divide by the time to get the rate (or by the rate to get the time).
Exampleउदाहरण
On a bill due in 9 months, BD = ₹1,344 and TD = ₹1,200. Rate?
Why it works, and when it failsयह क्यों काम करती है, और कब नहीं
Why:क्यों: BD = A × RT/100 and TD = A × RT/(100 + RT). Their ratio is (100 + RT)/100 = 1 + RT/100, whatever the face value.
Limits:सीमाएँ: Simple interest only, with BD and TD for the same bill and time.
Solved examplesहल किए गए उदाहरण
Answers and full solutions are shown. Hide them to test yourself first.उत्तर और पूरे हल दिखाए गए हैं। पहले खुद को परखने के लिए इन्हें छिपाइए।
Example 1उदाहरण 1 · Banker’s discount and banker’s gain · Easyआसान
A seed company in Bhopal holds a bill for ₹24,360 due 15 months from now. It gets the bill discounted at a bank at 4% per annum. What is the banker’s discount?
₹1,160
₹1,218
₹14,616
₹23,142
Answer:उत्तर:₹1,218
R × T = 4 × 15/12 = 5.
BD = 24,360 × 5/100 = ₹1,218.
Example 2उदाहरण 2 · Banker’s discount and banker’s gain · Mediumमध्यम
A printing press in Pune holds a bill for ₹1,95,700 due 9 months from now. At 4% per annum, what is the banker’s gain on the bill?
₹171
₹176.13
₹5,700
₹5,871
Answer:उत्तर:₹171
R × T = 3.
BD = 1,95,700 × 3/100 = ₹5,871.
TD = 1,95,700 × 3/103 = ₹5,700.
BG = ₹5,871 − ₹5,700 = ₹171.
Example 3उदाहरण 3 · Banker’s discount and banker’s gain · Hardकठिन
A spice exporter in Ranchi has a bill due 8 months from now. At 6% per annum, the banker’s gain on it is ₹224. What is the true discount?
₹8.96
₹466.67
₹5,600
₹5,824
Answer:उत्तर:₹5,600
R × T = 4.
TD = BG × 100/(RT) = 224 × 100/4 = ₹5,600.
Example 4उदाहरण 4 · Banker’s discount and banker’s gain · Mediumमध्यम
A garment unit in Surat holds a bill for ₹33,800 due 6 months from now. At 8% per annum, what is the banker’s gain on the bill?
₹52
₹54.08
₹1,300
₹1,352
Answer:उत्तर:₹52
R × T = 4.
BD = 33,800 × 4/100 = ₹1,352.
TD = 33,800 × 4/104 = ₹1,300.
BG = ₹1,352 − ₹1,300 = ₹52.
Example 5उदाहरण 5 · Banker’s discount and banker’s gain · Mediumमध्यम
A spice exporter in Indore holds a bill for ₹88,400 due 8 months from now. At 6% per annum, what is the banker’s gain on the bill?
₹136
₹141.44
₹3,400
₹3,536
Answer:उत्तर:₹136
R × T = 4.
BD = 88,400 × 4/100 = ₹3,536.
TD = 88,400 × 4/104 = ₹3,400.
BG = ₹3,536 − ₹3,400 = ₹136.
Example 6उदाहरण 6 · Banker’s discount and banker’s gain · Mediumमध्यम
A garment unit in Ranchi holds a bill for ₹18,550 due 9 months from now. At 8% per annum, what is the banker’s gain on the bill?
₹63
₹66.78
₹1,050
₹1,113
Answer:उत्तर:₹63
R × T = 6.
BD = 18,550 × 6/100 = ₹1,113.
TD = 18,550 × 6/106 = ₹1,050.
BG = ₹1,113 − ₹1,050 = ₹63.
Common mistakesआम गलतियाँ
Giving the true discount when the banker’s discount is asked; the bank charges interest on the face value, not on the present worth.
Taking BG as interest on BD instead of interest on TD.
Adding BD and TD to get the face value.
Frequently asked questionsअक्सर पूछे जाने वाले प्रश्न
Why is banker’s discount more than true discount?
The bank charges interest on the face value, which is bigger than the present worth. True discount is interest only on the present worth.
What is banker’s gain?
It is BD − TD, the bank’s extra profit over the fair discount. It equals the simple interest on the true discount for the same time and rate.
How do I find the face value from BD and TD?
Use A = BD × TD/(BD − TD). For BD = ₹1,344 and TD = ₹1,200: 1,344 × 1,200/144 = ₹11,200.