# 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:

Answer: Option

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.

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.

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.

Radhika said:
10 years ago

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?

Aneela said:
1 decade ago

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

Abc said:
1 decade ago

Is it solved the same way as simple interest?

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