Aptitude - Banker's Discount - Discussion

Discussion :: Banker's Discount - General Questions (Q.No.2)

2.

The banker's discount on Rs. 1600 at 15% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. The time is:

 [A]. 3 months [B]. 4 months [C]. 6 months [D]. 8 months

Explanation:

S.I. on Rs. 1600 = T.D. on Rs. 1680. Rs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is on Rs. 1600 at 15%. Time = 100 x 80 year = 1 year = 4 months. 1600 x 15 3

 Prateek said: (Oct 22, 2010) P.W. stands for? What is True Discount?

 Sundar said: (Oct 22, 2010) @Prateek PW - Present Worth. See: True Discount - Definition and Important Formulas

 Krishna said: (Mar 20, 2011) Please explain clearly. What is S.I, P.W? And the formulas.

 Amit said: (Mar 23, 2011) @ krishna- si= simple interest

 Prena said: (Nov 20, 2011) Is there any other alternative or shortcut way to solve this question?

 Ashish Garg said: (Dec 16, 2011) B.D= 1600*15*T/100=240T T.D=1680*15*T/100+15T NOW,B.D=T.D THUS T=1/3*12=4 MONTHS

 Sayan said: (Mar 6, 2012) 240T=1680*15*T/100+15T 240T=25200T/100+15T 24000T+3600T2=25200T T(24000+3600T)=25200T 24000+3600T=25200 3600T=25200-24000 T=1200/3600 T=1/3 T=4 Months

 Mansubh said: (May 9, 2012) Can we solve this by using P*R*T method.

 Swati Samaniya said: (Aug 4, 2013) Whats B.D ?

 M.Karthikeyan said: (Oct 8, 2013) I want to know about what is simple interest & compound interest and profit & loss?

 Sravanthi said: (May 26, 2014) Can any one explain me how the formulas of B.D and T.D are derived?

 Isha said: (Jun 14, 2014) B.D = bank discount and t.d = true discount.

 Varun Reddy said: (Jul 29, 2014) Can we solve with formula simple interest?

 Seema said: (Sep 30, 2014) What is the 80? anybody tell me.

 Ankit said: (Dec 25, 2014) @Seema. It is the simple interest due on the sum of 1600 @15%pa for 4 months period.

 Sukumar Satyen said: (Apr 29, 2015) Following is explanation: Given that, Banker's Discount (BD) is simple interest on Face Value of bill (F1), where F1 = Rs. 1600. True Discount (TD) is simple interest on Present Worth of Bill (PW), whose Face Value (F2) = Rs. 1680. And, from question, BD = TD...........equation (1). We know, BD = F1*T*R /100. => BD = 1600*T*15/100. => BD = 16*15*T...........equation (2). We know, PW = F2/{1+(T*R/100)} => PW = 1680/{1+(15*T/100)}...........equation (3). We know, TD = PW*T*R /100. => TD = PW*T*15/100. => TD = [1680/{1+(15*T/100)}]*15*T/100........... equation (4). We put value of equation (3) here. Using equation (1), (2) and (4). => 16*15*T = [1680/{1+(15*T/100)}]*15*T/100. => 16*15*T*100/(15*T) = [1680/{1+(15*T/100)}]. => 16*100 = [1680/{1+(15*T/100)}]. => {1+(15*T/100)} = 1680/1600. => (15*T/100) = (1680/1600)-1. => (15*T/100) = (1680-1600)/1600. => (15*T/100) = 80/1600 = 1/20. => T = 100/(15*20) = 1/3 years. => T = (1/3)*12 months. => T = 4 months. Thanks.

 Anisha said: (Jun 27, 2015) What is S.I.? And what is time's formula?

 Naaz said: (Jun 2, 2016) Can anyone explain me clearly, how did that 80 came?

 Anna said: (Jun 29, 2016) From, where the value of 100 comes?

 Hari Prasad said: (Sep 10, 2016) 1600 in 15% = 240. 1680 - 1600 = 80, 80/240 = 1/3. So, the answer is 12 months * 1/3 = 4months.

 Jiten said: (Dec 31, 2016) What is S.I?

 Shanthi said: (Mar 26, 2017) I'm not getting the answer. Can anyone explain me clearly?

 Abcd said: (Jun 9, 2017) @Jiten. S.I is Simple Interest.

 Navaraj said: (Jun 14, 2018) Why 1600 is taken in time calculation? If Td is 1680.

 Mithun Pk said: (Jul 24, 2018) I think T.D is 1600 and B.D is 1680. Then based on T.D formula this can be solved.

 Saurav said: (Jul 30, 2018) How did 240 come? Please explain.

 S. Jamesanderson said: (Aug 2, 2018) Please explain the solution with the shortcut method.

 Mahesh said: (Apr 3, 2019) 1600-15% = 240 1680-1600 = 80 80/240 = 1/3 *"4/12 = 1/3" * 4 is no of months /12 is total months, So, the answer is = 4 Months.

 Jasmine said: (Oct 7, 2020) What is the formula for time? Please, anyone, tell me.

 Nahwera David said: (Apr 19, 2021) Anyone help me to get it clearly?

 Rumesh said: (Jun 17, 2021) Formula for T.D = Amount * R * T /100 + (R*T). Formula for B.D = Amount * R * T /100. Given data: B.D. 's amount = 1600, T.D 's amount = 1680, R = 15 %, T = ?. B.D = T.D ( given B.D is same as T.D). Amount * R * T/100 = Amount * R * T/100 + (R*T), 1600 * 15 * T/100 = 1680 * 15 * T/100 + ( 15 * T), On simplification we get, T = 1/3 years. To convert years to months, multiply by 12. T = 1/3 * 12 = 4 months.

 Sumaira said: (Jul 25, 2021) @Mahesh. Can you explain how 1600_15% is equal to 240? Anyone else please explain this.