Aptitude - Banker's Discount - Discussion

Following is explanation:

Given that,

Banker's Discount (BD) is simple interest on Face Value of bill (F1), where F1 = Rs. 1600.

True Discount (TD) is simple interest on Present Worth of Bill (PW), whose Face Value (F2) = Rs. 1680.

And, from question, BD = TD...........equation (1).

We know, BD = F1*T*R /100.

=> BD = 1600*T*15/100.
=> BD = 16*15*T...........equation (2).

We know, PW = F2/{1+(T*R/100)}
=> PW = 1680/{1+(15*T/100)}...........equation (3).

We know, TD = PW*T*R /100.
=> TD = PW*T*15/100.
=> TD = [1680/{1+(15*T/100)}]*15*T/100........... equation (4).

We put value of equation (3) here.

Using equation (1), (2) and (4).

=> 16*15*T = [1680/{1+(15*T/100)}]*15*T/100.

=> 16*15*T*100/(15*T) = [1680/{1+(15*T/100)}].

=> 16*100 = [1680/{1+(15*T/100)}].

=> {1+(15*T/100)} = 1680/1600.

=> (15*T/100) = (1680/1600)-1.

=> (15*T/100) = (1680-1600)/1600.

=> (15*T/100) = 80/1600 = 1/20.

=> T = 100/(15*20) = 1/3 years.

=> T = (1/3)*12 months.

=> T = 4 months.

Thanks.

Formula for T.D = Amount * R * T /100 + (R*T).
Formula for B.D = Amount * R * T /100.

Given data:
B.D. 's amount = 1600,
T.D 's amount = 1680,
R = 15 %,
T = ?.
B.D = T.D ( given B.D is same as T.D).

Amount * R * T/100 = Amount * R * T/100 + (R*T),
1600 * 15 * T/100 = 1680 * 15 * T/100 + ( 15 * T),

On simplification we get, T = 1/3 years.
To convert years to months, multiply by 12.
T = 1/3 * 12 = 4 months.

@Prateek

PW - Present Worth.

See: True Discount - Definition and Important Formulas

240T=1680*15*T/100+15T
240T=25200T/100+15T
24000T+3600T2=25200T
T(24000+3600T)=25200T
24000+3600T=25200
3600T=25200-24000
T=1200/3600
T=1/3
T=4 Months

1600-15% = 240
1680-1600 = 80
80/240 = 1/3 *"4/12 = 1/3" * 4 is no of months /12 is total months,
So, the answer is = 4 Months.

1600 in 15% = 240.
1680 - 1600 = 80,
80/240 = 1/3.

So, the answer is 12 months * 1/3 = 4months.

I want to know about what is simple interest & compound interest and profit & loss?

@Mahesh.

Can you explain how 1600_15% is equal to 240?

Anyone else please explain this.

@Seema.

It is the simple interest due on the sum of 1600 @15%pa for 4 months period.

I think T.D is 1600 and B.D is 1680.

Then based on T.D formula this can be solved.