Aptitude - Banker's Discount - Discussion

Discussion Forum : Banker's Discount - General Questions (Q.No. 11)
11.
The present worth of a sum due sometime hence is Rs. 576 and the banker's gain is Rs. 16. The true discount is:
Rs. 36
Rs. 72
Rs. 48
Rs. 96
Answer: Option
Explanation:

T.D. = P.W. x B.G. = 576 x 16 = 96.

Discussion:
9 comments Page 1 of 1.

Ankita said:   1 decade ago
What is T.D , P.W , B.G?

Kanika said:   1 decade ago
can any body explain how is d formula obtained?

Pramod said:   1 decade ago
P.W is Present Worth. B.G is Bankers Gain.

Maria said:   1 decade ago
T.D is True Discount

KING said:   1 decade ago
This formula is obtained by the banker gain formula i.e B.G=[T.D]*[T.D]/P.W

Yeksh said:   1 decade ago
What does present worth mean?

Suman Roy said:   1 decade ago
How formula is obtained ?

Anshika said:   10 years ago
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?

SUKUMAR SATYEN said:   9 years ago
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.

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