Aptitude - Banker's Discount - Discussion
Discussion Forum : Banker's Discount - General Questions (Q.No. 2)
2.
The banker's discount on Rs. 1600 at 15% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. The time is:
Answer: Option
Explanation:
S.I. on Rs. 1600 = T.D. on Rs. 1680.
Rs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is on Rs. 1600 at 15%.
| Time = |
 |
100 x 80 |  year |
= | 1 | year = 4 months. |
| 1600 x 15 | 3 |
Discussion:
33 comments Page 3 of 4.
Sukumar Satyen said:
1 decade ago
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.
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.
Ankit said:
1 decade ago
@Seema.
It is the simple interest due on the sum of 1600 @15%pa for 4 months period.
It is the simple interest due on the sum of 1600 @15%pa for 4 months period.
Seema said:
1 decade ago
What is the 80? anybody tell me.
Isha said:
1 decade ago
B.D = bank discount and t.d = true discount.
Sravanthi said:
1 decade ago
Can any one explain me how the formulas of B.D and T.D are derived?
M.KARTHIKEYAN said:
1 decade ago
I want to know about what is simple interest & compound interest and profit & loss?
Swati samaniya said:
1 decade ago
Whats B.D ?
Sayan said:
1 decade ago
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
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
Ashish Garg said:
1 decade ago
B.D= 1600*15*T/100=240T
T.D=1680*15*T/100+15T
NOW,B.D=T.D
THUS T=1/3*12=4 MONTHS
T.D=1680*15*T/100+15T
NOW,B.D=T.D
THUS T=1/3*12=4 MONTHS
Prena said:
1 decade ago
Is there any other alternative or shortcut way to solve this question?
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