True Discountवास्तविक बट्टाquestions and answersप्रश्न और उत्तर
If you owe money a year from now, paying today should cost less. The fair amount to pay today is the present worth, and the saving is the true discount. Both come from simple interest run backwards.
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How true discount worksवास्तविक बट्टा को समझिए
Present worth (PW) is the sum which, lent today at the given simple interest rate, grows to exactly the amount due (A) on the due date. So A = PW × (100 + RT)/100, which gives PW = 100A/(100 + RT).
True discount (TD) is the difference A − PW. Because PW grows into A, the true discount is also the simple interest on the present worth: TD = PW × R × T/100. This is the check to run on every answer.
Time must be in years. A sum due in 9 months at 8% has R × T = 8 × 9/12 = 6, so PW = 100A/106. Many options in exam papers come from using 9 instead of 9/12.
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।
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True discount is interest on the present worth
Use it when:कब इस्तेमाल करें: Any present-worth or true-discount question, or to check an option before marking it.
Why it works, and when it failsयह क्यों काम करती है, और कब नहीं
Why:क्यों: PW grows to A at simple interest, so A = PW(1 + RT/100). Then A − PW = PW × RT/100, which is the interest on PW, and dividing A by (100 + RT)/100 gives PW.
Limits:सीमाएँ: Assumes simple interest, the usual convention for true discount. It does not apply to compound-interest present value.
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.
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 · True discount and present worth · Easyआसान
Saanvi has to pay ₹14,112 for spices bought on credit, due 3 years from now. Money is worth 4% per annum simple interest. What is the true discount?
₹1,512
₹1,693.44
₹1,924.36
₹12,600
Answer:उत्तर:₹1,512
R × T = 12.
PW = 100 × 14,112/(100 + 12) = ₹12,600.
TD = ₹14,112 − ₹12,600 = ₹1,512.
Check: simple interest on ₹12,600 at 4% for 3 years = ₹1,512.
Example 2उदाहरण 2 · True discount and present worth · Mediumमध्यम
Ananya has to pay ₹20,188 to a fertiliser supplier, due 3 months from now. Money is worth 12% per annum simple interest. What is the present worth of the debt?
₹588
₹14,844.12
₹19,582.36
₹19,600
Answer:उत्तर:₹19,600
R × T = 3.
PW = 100 × 20,188/(100 + 3) = ₹19,600.
TD = ₹20,188 − ₹19,600 = ₹588.
Check: simple interest on ₹19,600 at 12% for 3 months = ₹588.
Example 3उदाहरण 3 · True discount and present worth · Hardकठिन
A trader in Jaipur owes a sum for a used tractor, due 6 months from now. At 12% per annum simple interest, the true discount on it is ₹1,062. What is the sum due?
₹2,537
₹16,638
₹17,700
₹18,762
Answer:उत्तर:₹18,762
R × T = 12 × 6/12 = 6.
PW = TD × 100/(RT) = 1,062 × 100/6 = ₹17,700.
Sum due = PW + TD = ₹17,700 + ₹1,062 = ₹18,762.
Example 4उदाहरण 4 · True discount and present worth · Mediumमध्यम
Meera has to pay ₹1,284 for a batch of saris, due 6 months from now. Money is worth 14% per annum simple interest. What is the present worth of the debt?
₹84
₹697.83
₹1,194.12
₹1,200
Answer:उत्तर:₹1,200
R × T = 7.
PW = 100 × 1,284/(100 + 7) = ₹1,200.
TD = ₹1,284 − ₹1,200 = ₹84.
Check: simple interest on ₹1,200 at 14% for 6 months = ₹84.
Example 5उदाहरण 5 · True discount and present worth · Mediumमध्यम
Isha has to pay ₹2,884 to a cement dealer, due 3 months from now. Money is worth 12% per annum simple interest. What is the present worth of the debt?
₹84
₹2,120.59
₹2,797.48
₹2,800
Answer:उत्तर:₹2,800
R × T = 3.
PW = 100 × 2,884/(100 + 3) = ₹2,800.
TD = ₹2,884 − ₹2,800 = ₹84.
Check: simple interest on ₹2,800 at 12% for 3 months = ₹84.
Example 6उदाहरण 6 · True discount and present worth · Mediumमध्यम
Harpreet has to pay ₹15,985 for a batch of saris, due 18 months from now. Money is worth 10% per annum simple interest. What is the true discount?
₹2,085
₹2,397.75
₹10,276.07
₹13,900
Answer:उत्तर:₹2,085
R × T = 15.
PW = 100 × 15,985/(100 + 15) = ₹13,900.
TD = ₹15,985 − ₹13,900 = ₹2,085.
Check: simple interest on ₹13,900 at 10% for 18 months = ₹2,085.
Common mistakesआम गलतियाँ
Taking simple interest on the amount due; that is the banker’s discount, which is larger than the true discount.
Answering with the present worth when the true discount is asked, or the other way round.
Using the time in months as if it were years.
Frequently asked questionsअक्सर पूछे जाने वाले प्रश्न
What is the difference between present worth and true discount?
Present worth is what you pay today to settle a debt due later. True discount is how much less that is than the amount due: TD = A − PW.
Why is true discount the interest on present worth and not on the amount?
Because the present worth is the money that earns interest until the due date. The interest it earns is exactly what turns it into the amount due.
Is true discount asked in bank and SSC exams?
It is less common now than percentage or interest, but it still appears in some bank, insurance and placement papers, often paired with banker’s discount.