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BANKER'S DISCOUNT
IMPORTANT CONCEPTS
Banker's Discount : Suppose a merchant A buys goods worth, say Rs. 10,000 from another merchant B at a credit of say 5 months. Then, B prepares a bill, called the bill of exchange. A signs this bill and allows B to withdraw the amount from his bank account after exactly 5 months.
The date exactly after 5 months is called nominally due date. Three days (known as grace days) are added to it to get a date, known as legally due date.
बैंकर की छूट: मान लीजिए कि एक व्यापारी ए सामान के लायक खरीदता है, रु। 5 महीने के क्रेडिट पर एक और व्यापारी बी से 10,000। फिर, बी एक बिल तैयार करता है, जिसे एक्सचेंज बिल कहा जाता है। इस बिल पर एक संकेत है और बी को 5 महीने के बाद अपने बैंक खाते से राशि वापस लेने की अनुमति देता है।
Suppose B wants to have the money before the legally due date. Then he can have the money from the banker or a broker, who deducts S.I. on the face value (i.e., Rs. 10,000 in this case) for the period from the date on which the bill was discounted (i.e., paid by the banker) and the legally due date. This amount is known as Banker's Discount (B.D.) Thus, B.D. is the S.I. on the face value for the period from the date on which the bill was discounted and the legally due date.
5 महीने के ठीक बाद की तारीख को नाममात्र देय तिथि कहा जाता है। कानूनी रूप से देय तिथि के रूप में जाना जाने वाला दिनांक प्राप्त करने के लिए तीन दिन (अनुग्रह दिवस के रूप में जाना जाता है) इसमें जोड़ा जाता है।
मान लीजिए बी कानूनी रूप से देय तिथि से पहले पैसा लेना चाहता है। उसके बाद वह बैंकर या ब्रोकर से धन प्राप्त कर सकता है, जिसने बिल को छूट दी गई थी (यानी बैंकर द्वारा भुगतान की गई तारीख) की अवधि के लिए चेहरे मूल्य (यानि, इस मामले में 10,000 रुपये) पर एसआई को घटाया जाता है। और कानूनी रूप से देय तिथि। यह राशि बैंकर डिस्काउंट (बीडी) के रूप में जानी जाती है, इस प्रकार, बी.डी. जिस तारीख को बिल छूट दी गई थी और कानूनी रूप से देय तिथि से उस अवधि के लिए अंकित मूल्य पर एसआई है।
Banker's Gain (B.G.) = (B.D.) - (T.D.) for the unexpired time.
Note : When the date of the bill is not given, grace days are not to be added.
IMPORTANT FORMULAE
1. B.D. = S.I. on bill for unexpired time.
2. B.G. = (B.D.)-(T.D.) = S.I. on T.D. =(T.D)2 /P.W.
3. T.D. = (P.W.xB.G.)
4. B.D. =[(Amount *Rate *Time)/100]
5.Amount=[(B.D. x T.D.)/(B.D.-T.D.)]
6. T.D.= [(Amount x Rate x Time)/(100+(Rate*Time))]
7. T.D.=[( B.G. x 100)/(Rate x Time)]
SOLVED EXAMPLES
Ex. 1. A bill for Rs. 6000 is drawn on July 14 at 5 months. It is discounted on 5th October at 10%. Find the banker's discount, true discount, banker's gain and the money that the holder of the bill receives.
14 जुलाई को 6000 रुपये के लिए एक बिल 14 महीने पर तैयार किया जाता है। इसे 5 अक्टूबर को 10% पर छूट दी गई है। बैंकर की छूट, सच्ची छूट, बैंकर का लाभ और बिल धारक को प्राप्त धन प्राप्त करें।
Solution:
Face value of the bill = Rs. 6000.
Date on which the bill was drawn = July 14 at 5 months. Nominally due date = December 14.
Legally due date = December 17.
Date on which the bill was discounted = October 5.
Unexpired time : Oct. Nov. Dec.
26 + 30 + 17 = 73 days =1/ 5Years
B.D. = S.I. on Rs. 6000 for 1/5 year
= Rs. (6000 x 10 x1/5 x1/100)= Rs. 120.
T.D. = Rs.[(6000 x 10 x1/5)/(100+(10*1/5))]
=Rs.(12000/102)=Rs. 117.64.
B.G. = (B.D.) - (T.D.) = Rs. (120 - 117.64) = Rs. 2.36.
Money received by the holder of the bill = Rs. (6000 - 120)
= Rs. 5880.
Ex. 2. If the true discount on a certain sum due 6 months hence at 15% is Rs. 120,what is the banker's discount on the same sum for the same time and at the same rate?
यदि वजह से 6 महीने इसलिए 15% पर एक निश्चित राशि पर सच छूट रुपये है। 120, एक ही समय के लिए उसी राशि पर बैंकर की छूट क्या है और उसी पर दर क्या है?
Solution:
B.G. = S.I. on T.D.
= Rs.(120 x 15 x 1/2 x 1/100)
= Rs. 9.
(B.D.) - (T.D.) = Rs. 9.
B.D. = Rs. (120 + 9) = Rs. 129.
Ex. 3. The banker's discount on Rs. 1800 at 12% per annum is equal to the true discount on Rs. 1872 for the same time at the same rate. Find the time.
बैंकर का सालाना 12% पर 1800Rs छूट सच के बराबर है
एक ही दर पर एक ही समय के लिए पर 1872Rs छूट। समय का पता लगाएं।
Solution:
S.I. on Rs. 1800 = T.D. on Rs. 1872.
P.W. of Rs. 1872 is Rs. 1800.
Rs. 72 is S.I. on Rs. 1800 at 12%.
Time =[(100 x 72)/ (12x1800)]year
1/3year = 4 months.
Ex. 4. The banker's discount and the true discount on a sum of money due 8 months hence are Rs. 120 and Rs. 110 respectively. Find the sum and the rate percent.
बैंकर की छूट और 8 महीने के कारण धनराशि पर सच्ची छूट क्रमशः 120 रुपये और 110 रुपये है। योग और दर प्रतिशत खोजें।
Solution:
Sum =[( B.D.*T.D.)/(B.D.-T.D.)]
= Rs.[(120x110)/(120-110)]
= Rs. 1320.
Since B.D. is S.I. on sum due, so S.I. on Rs. 1320 for 8 months is Rs. 120.
Rate =[(100 x120)/( 1320 x 2/3)%
= 13 7/11%.
Ex. 5. The present worth of a bill due sometime hence is Rs. 1100 and the true discount on the bill is Rs. 110. Find the banker's discount and the banker's gain.
कुछ समय के लिए बिल का वर्तमान मूल्य 1100 रुपये है और बिल पर वास्तविक छूट 110 रुपये है। बैंकर की छूट और बैंकर के लाभ को खोजें।
Solution:
T.D. =(P.W.*B.G)
B.G. =(T.D.)2/ P.W.
= Rs.[(110x110)/ 1100]
= Rs. 11.
B.D.= (T.D. + B.G.) = Rs. (110 + 11) = Rs. 121.
Ex. 6. The banker's discount on Rs. 1650 due a certain time hence is Rs. 165. Find the true discount and the banker's gain.
1650 रुपये पर बैंकर की छूट निश्चित समय के कारण 165 रुपये है। सही छूट और बैंकर के लाभ को खोजें।
Solution:
Sum = [(B.D.xT.D.)/ (B.D.-T.D.)]
= [(B.D.xT.D.)/B.G.]
T.D./B.G. = Sum/ B.D.
=1650/165
=10/1
Thus, if B.G. is Re 1, T.D. = Rs. 10.
If B.D.is Rs. ll, T.D.=Rs. 10.
If B.D. is Rs. 165, T.D. = Rs. [(10/11)xl65]
=Rs.150
And, B.G. = Rs. (165 - 150) = Rs, 15.
Ex. 7. What rate percent does a man get for his money when in discounting a bill due 10 months hence, he deducts 10% of the amount of the bill?
10 महीने के कारण बिल छूटने पर एक व्यक्ति को अपने पैसे के लिए कितना दर प्रतिशत मिलता है, तो वह बिल की राशि का 10% घटा देता है?
Solution:
Let amount of the bill = Rs.100
Money deducted =Rs.10
Money received by the holder of the bill = Rs.100-10 = Rs.90
SI on Rs.90 for 10 months = Rs.10
Rate =[(100*10)/(90*10/12)%=13 1/3%
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