Aptitude - Banker's Discount - Discussion

Discussion :: Banker's Discount - General Questions (Q.No.9)

9. 

The banker's gain on a bill due 1 year hence at 12% per annum is Rs. 6. The true discount is:

[A]. Rs. 72
[B]. Rs. 36
[C]. Rs. 54
[D]. Rs. 50

Answer: Option D

Explanation:

T.D. = B.G. x 100 = Rs. 6 x 100 = Rs. 50.
R x T 12 x 1


Abc said: (Nov 14, 2011)  
Is it solved the same way as simple interest?

Aneela said: (Jul 25, 2013)  
Can you say me how the discount is calculated. Is there any formulae for calculating it?

Srira said: (Oct 6, 2014)  
Can you say me how the B.G is calculating?

Radhika said: (Oct 6, 2014)  
Please explain this question and give another easy method.

Sukumar Satyen said: (Apr 30, 2015)  
Following is detailed explanation:

Banker's Gain (BG) is difference between Banker's Discount (BD) and True Discount (TD).

=> BG = BD - TD.

=> 6 = (F*R*T/100) - (PW*R*T/100).
=> 6 = (R*T/100)(F - PW).
=> 6 = (12/100)(F - PW).
=> 6*100/12 = F - PW.

=> F - PW = 50..........equation (1).

We know, PW = F/{1+(T*R/100)}

=> F-[ F/{1+(T*R/100)}] = 50.
=> F-[ F/{1+(12/100)}] = 50.

=> F-[ F/{112/100 }] = 50.
=> F-[ F/{112/100 }] = 50.

=> F-[ 100 F/112 ] = 50.
=> (112 F-100 F)/112 = 50.

=> 12 F/112 = 50.
=> F = 50*112/12.

Next, we need to calculate Present Worth (PW).

=> PW = F/{1+(T*R/100)}.
=> PW = (50*112/12)/{1 + (12/100)}.

=> PW = (50*112/12)/{112/100}.
=> PW = (50*112*100)/(112*12).

=> PW = 50*100/12.

Present Worth (PW) can also be calculated from equation (1):

=> F-PW = 50.
=> PW = F-50.

=> PW = 50*112/12-50.
=> PW = (50*112-50*12)/12.

=> PW = 50*(112-12)/12.
=> PW = 50*100/12.

NOW, we can calculate True Discount (TD), which is simple interest on Present Worth (PW).

=> TD = PW*R*T/100.
=> TD = (50*100/12)*(12/100).
=> TD = Rs. 50.

Thanks.

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