Aptitude - Banker's Discount - Discussion

Discussion :: Banker's Discount - General Questions (Q.No.1)

1. 

The banker's discount on a bill due 4 months hence at 15% is Rs. 420. The true discount is:

[A]. Rs. 400
[B]. Rs. 360
[C]. Rs. 480
[D]. Rs. 320

Answer: Option A

Explanation:

T.D.
= B.D. x 100
100 + (R x T)
= Rs. 420 x 100
100 + 15 x 1
3
= Rs. 420 x 100
105
= Rs. 400.

Ramkumar said: (Aug 17, 2010)  
How T = 1/3?

Mayuri said: (Aug 20, 2010)  
How to find in shortcut way?

Raja Shekar said: (Sep 3, 2010)  
What is the T stands for?

Sundar said: (Sep 3, 2010)  
Hi All,

Here T stands for Time or Number of Years.

Why T = 1/3?

Because we can write 4 months as 1/3 years. (Ref: 4/12 = 1/3)

Hope you understand. Have a nice day guys!

Vinoth said: (Nov 10, 2010)  
How we can take 15% is rate?

Saleem said: (Jan 29, 2011)  
short cut:

p*r*t

420*15%*4/12 = 20

420-20 = 400

Jyothi said: (Feb 9, 2011)  
How comes this formula T.D. = B.D. x 100 / 100+(R*T)


Atually T.D = Amout*rate*time / 100+(R*T)

Yuri said: (Feb 19, 2011)  
Same question as Jyotiii.

Achyuth said: (May 7, 2011)  
Why we use 1/3 for percentage?

Bhargav said: (May 23, 2011)  
What does T.D. & P.W. stands for ???

Sundar said: (May 23, 2011)  
TD - True Discount
PW - Present Worth

Mannoj Kumar said: (Jun 11, 2011)  
How comes this formula T.D. = B.D. x 100 / 100+(R*T)


Atually T.D = Amout*rate*time / 100+(R*T)

--------------------------------------------------------------------------------
B.D = amount*rate*time/100

T.D = (amount*rate*time/100)*100/100+(rate*time)
= amount*rate*time/100+(rate*time)

Siva said: (Jul 12, 2011)  
Why we put 100?

Jessi said: (Jul 19, 2011)  
What is the need to sub 20. Saleem said in short cut.

K Shravanreddy said: (Aug 2, 2011)  
Actually what is the difference between T. D, S. I and B. D.

Siraj said: (Aug 3, 2011)  
How it comes 420*15%*4/12 =20 as saleem said actually answer is 21

Amit said: (Nov 11, 2011)  
Can anyone tell me a clear definition of true discount and bankers discount. I have a lot of confusion with the theory.

Please. I have to appear in a test before 19th nov.

Muhammad Asif said: (Feb 5, 2012)  
Easy solution
15% rate is for one year so we have to cslculate for 1/3 so its become 5% of 15% 420*100/105=400

Jai Gupta said: (May 23, 2012)  
How to come B.D.=(A*R*T)/100;
T.D.=(A*R*T)/[100+(R*T)];
THEN T.D.=[(A*R*T)*(100/100)]/[100+(R*T)];
T.D.=[((A*R*T)/(100))*100]/[100+(R*T)];
T.D.=BD.*100/[100+(R+T)]

Divya said: (Sep 8, 2012)  
How T=1/3 ?

Anam Charan Patra said: (Feb 22, 2013)  
How to found short way to solve this problem?

Preeti said: (Jul 24, 2013)  
B.D = Banker's Discount.
T.D = True Discount.
A = Amount.
R = Rate.
T = Time.

T.D=A*R*T/(100+RT).

B.D=A*R*T/100.

Divide by 100 in numerator and denominator In T.D.

T.D=[(A*R*T)/100]/[(100+RT)*100].

In T.D formula substitute B.D formula.

T.D=[B.D*100]/[100+(R*T)].

Sawma said: (Aug 9, 2013)  
It was written in the important formulas that,

T.D = B.G x 100/Rate x Time.

Why you use another formula?

Karthick said: (Aug 28, 2013)  
How to found short way to solve this problem?

Lakshmi said: (Sep 19, 2013)  
What is B. D please give me the explanation?

Piyushkantidhara said: (Sep 22, 2013)  
What is the difference between true discount and banker discount?

Suvrajit Samal said: (Jul 24, 2014)  
Please tell me how this formula is derived?

Ramapati said: (Aug 21, 2014)  
What is the difference between true discount and banker discount?

Kiran said: (Aug 26, 2014)  
-> True discount means the simple interest obtained after the nominal date.

-> If one wants to withdraw money before the due date then banker will deduct some amount from the face value and give i.e one will get less than the face value amount.

-> Suppose x is the face value,if one withdraws after due date he will get (face value + interest),->i.e true discount.

-> If one withdraws before the due date then he will get (face value-some amount)(it some amount it may be equal to S.I)->i.e bankers discount.

-> Therefore,Banker's Gain= True discount-Bankers discount.

Baku Krishnas said: (Sep 11, 2014)  
T = No.of mints\ total year mints.
T = 4\12.
T = 1\3 dudes.

Prathyu said: (Nov 8, 2014)  
Thanks @Kiran for explaining but I have a small doubt you said true discount is equal to simple interest.

But you said again is equal to face value+ simple interest. I didn't understand once explain that.

M.Shoaib said: (Nov 20, 2014)  
This explanation is just for @Lakshmi's confusion,

Very simple, B.D stands for banker discount, a fix amount which is given by bank to its client on its deposit,

Got it @Lakshmi.

Bhanu said: (Mar 5, 2015)  
Why we take T=1/3?

Sukumar Satyen said: (Apr 29, 2015)  
Following is explanation, and may be a shortcut for few students:

Banker's Discount (BD) is simple interest on Face Value of Bill (F).

Given that, BD = Rs. 420, Time (T) = 4/12 year, Interest Rate (R) = 0.15.

True Discount (TD) is simple interest on Present Worth (PW).

We know, BD = F*T*R/100 = 420.

=> F = BD*100/T*R .
=> F = 420*100*12/(4*15).
=> F = 420*20.

We know, PW = F/{1+(T*R/100)}
=> PW = 420*20*100/105.
=> PW = 4*20*100.

We know, TD = PW*T*R/100.
=> TD = 4*20*100*4*15/(100*12).
=> TD = Rs. 400.

Thanks.

Girish said: (Aug 31, 2015)  
I didn't understand TD and BD and BG please anyone explain me?

Naveed Irshad said: (Sep 1, 2015)  
Thanks for all who mention the answers here.

Mahabur Alam said: (Sep 5, 2015)  
I = P*N*R.

Here I = Interest.

P = Capital.
N = Time.
R = Rate.

Let capital=x.

(420-x) = x*(4/12)*(15/100).

x = 400 answer.

Mayur said: (Oct 9, 2015)  
How can get 105?

Deekshitha said: (Jul 15, 2016)  
How T is 1/3? Please tell me.

Lokambika said: (Jul 25, 2016)  
Bill due is 4 months and for a year, total number of months is 12. So 4/12 = 1/3.

Biswajit Sethy said: (Aug 15, 2016)  
Here T stands for Time or Number of Years.

Why T = 1/3?

Because we can write 4 months as 1/3 years. (Ref: 4/12 = 1/3)

Manu said: (Aug 24, 2016)  
Somebody, please explain why TD formula 3time, and when to use, how to use it?

Before solving this question, I saw formulas but TD has three different way, confused and as per the TD FORMULA how 100 comes in formula?

Sreenivasulu said: (Aug 29, 2016)  
How the formula exist for amount = bd * td/bd - td?

Anu said: (Sep 3, 2016)  
How can we take rate = 15% directly?

Mollah said: (Oct 24, 2016)  
Nice question and excellent solution. Thanks!

Raama said: (Oct 29, 2016)  
How can we define T.D other than the formula, just like B.D?

Sweety said: (Nov 21, 2016)  
How 4\12 came? Explain me.

Svs said: (Jan 11, 2017)  
How 1/3 came? Not getting this.

N.Rajashekar said: (Jan 16, 2017)  
How 105 came?

Smitha said: (Jan 17, 2017)  
1/3 because they said 4 months.

We know that 12months = 1 year hence,
4months = ?
Which is (4months * 1year) ÷ 12months.
Which is 1/3 year.

Naimur Rahman said: (Jan 29, 2017)  
Good answer @Mahabur Alam.

Tausif said: (Mar 30, 2017)  
Can anyone discuss it in shortcut method?

Bharath Chan said: (Apr 3, 2017)  
Hi, all.

The true discount is initial amount Rs.400 (deposit on bank).

The banker's discount is the sum of amount and interest of the amount at particular interest rate (15%).

Rs.420 = 400 + (400x.15x(1/3)) = 400+20.

Jaspreet Singh said: (Apr 8, 2017)  
Sir, why I am getting 21?

please help me out 420*15%*4/12 is it the right way I am doing but still, my answer is 21 and your getting 20 please help me.

Thanks in advance.

Asg said: (Jun 23, 2017)  
Thanks for the explanation.

Priti said: (Oct 4, 2017)  
How 420*100/105 =400? please explain anyone.

Gopi said: (Dec 12, 2017)  
Thanks for explaining it.

Nivetha said: (Dec 13, 2017)  
420*100 = 42000,
42000 / (divide)105=400.

Ashish said: (Jan 30, 2018)  
B.G= S.I on T. D.
B.G=(T.D*R*T)/100.
B.D-T.D=(T.D*R*T)/100.
T.D+(T.D*R*T)/100=B.D.
T.D(100+R*T)/100=B.D.
T.D=B.D*100/(100+R*T).

Nanthini said: (Mar 5, 2018)  
Please, anyone explain me easily.

Yuga said: (May 14, 2018)  
Can anyone explain the problem, please?

Yasmeen said: (Jun 21, 2018)  
What about 105 how it comes?

Roshu said: (Aug 8, 2018)  
Actually BD=amt*rate*time/100.

TD=amt*rate*time/100+(rate*time).
BD *100=amt*rate*time.
we are substituting the amt*rate*time in TD with BD*100 from the above step,
so TD=BD*100/100+(rate*time).
so TD=420*100/100+(15*1/3).
We write 4 months as 1/3 because the time should be expressed in terms of years,so 4/12=1/3.
Thus we get 420*100/105=400.

Hope this helps.

Skiezz said: (Aug 22, 2018)  
BD=(A*R*T)/100.
TD=(A*R*T)/100+(R*T),
TD=BD*100/100+(R*T),
{BD*100= (A*R*T)/100*100}.

That's why BD*100=A*R*T.

Lavanya Katturoju said: (Oct 30, 2018)  
How 100 + (15 * 1/3) is 105? Plase explain.

Jubair said: (Jan 16, 2019)  
I think it will be too much easy if we take this as present value and future value.
Here banker's discount on a bill due 4 months hence at 15 % is RS 420, this 420 is the future value which we will get after 4 months. But what is the present value of that 420 is the true discount and the required answer.

So we can solve it solve it in Pv formula where,

PV = FV /(1+rn).
= 420 /1+ (15/100 * 4/12),
= 420 * 100/105,
= 400.

we can also take it as amount which is 420.
so P = 420 * 100/ (n*r)+100,
= 420 * 100/105,
= 400.

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