Aptitude - Banker's Discount - Discussion

Following is explanation:

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

=> BD = F*R*T/100.

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

=> BG = BD - TD.
=> 16 = BD - TD....equation (1).

Given that,

Present Worth (PW) = Rs. 576.

True Discount (TD) is to be found out, which is simple interest on Present Worth (PW).

We know that,

=> TD = PW*T*R/100.
=> TD = 576*T*R/100....equation (2).

From equation (1) & (2),

=> 16 = (F*R*T/100) - (576*T*R/100).
=> 16 = (F-576)*(R*T/100)....equation (3).

We know, PW = F/[1+(T*R/100)].

=> PW*[1+(T*R/100)] = F.
=> 576*[1+(T*R/100)] = F.

=> [1+(T*R/100)] = F/576.
=> (T*R/100) = (F/576)-1.

=> (T*R/100) = (F-576)/576....equation (4).

From equation (3) & (4),

=> 16 = (F-576)*(F-576)/576.
=> 16*576 = (F-576)*(F-576).

=> square root of (16*576) = (F-576).
=> 576±96 = F.

=> F = 672 or 480.

We take, F = 672.

From equation (2) & (4),

=> TD = 576*{(F-576)/576}.
=> TD = 672-576 = Rs. 96.

Here, F = 480 is not taken otherwise, TD would be negative.

Thanks.

How these all formulas on bankers discount and true discount are obtained? ate they baseless. Is there any existence of these type of formula in mathematics?

How formula is obtained ?

What does present worth mean?

This formula is obtained by the banker gain formula i.e B.G=[T.D]*[T.D]/P.W

T.D is True Discount

P.W is Present Worth. B.G is Bankers Gain.

can any body explain how is d formula obtained?

What is T.D , P.W , B.G?