# Aptitude - Banker's Discount - Discussion

Discussion Forum : 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:
Rs. 72
Rs. 36
Rs. 54
Rs. 50
Explanation:

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

Discussion:
6 comments Page 1 of 1.

Jamshaid said:   2 years ago
@All.

Simply, the solution is;
Sum = Rs.6/12% = 500.
TD = 500/1.12 * 0.12 = (500/112)*12 = 53.57.

Sukumar Satyen said:   9 years ago
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.

Please explain this question and give another easy method.
(1)

Srira said:   10 years ago
Can you say me how the B.G is calculating?