Aptitude - Banker's Discount - Discussion

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.

@All.

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

Can you say me how the discount is calculated. Is there any formulae for calculating it?

Please explain this question and give another easy method.

Is it solved the same way as simple interest?

Can you say me how the B.G is calculating?