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

Answer: Option B

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.

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