Aptitude - Simple Interest - Discussion
Discussion Forum : Simple Interest - General Questions (Q.No. 9)
9.
A sum of Rs. 725 is lent in the beginning of a year at a certain rate of interest. After 8 months, a sum of Rs. 362.50 more is lent but at the rate twice the former. At the end of the year, Rs. 33.50 is earned as interest from both the loans. What was the original rate of interest?
Answer: Option
Explanation:
Let the original rate be R%. Then, new rate = (2R)%.
Note:
Here, original rate is for 1 year(s); the new rate is for only 4 months i.e. 
year(s).
 |
 |
725 x R x 1 |  |
+ | |
362.50 x 2R x 1 | |
= 33.50 |
| 100 | 100 x 3 |
(2175 + 725) R = 33.50 x 100 x 3
(2175 + 725) R = 10050
(2900)R = 10050
| R = |
10050 | = 3.46 |
| 2900 |
Original rate = 3.46%
Discussion:
97 comments Page 2 of 10.
Vignesh said:
8 years ago
There are 2 loan consider A(725) and B(362.50). Loan A is taken for 1 year with some interest (R), at the end of eight-month another loan is taken which is B with interest (2R). That is one loan is for 1 year and another loan is for 4 months. By the end of the year SI = loan for one year(725) + loan for 4 months(362.5) ie 725 x R x 1 /100+ 362.50 x 2R x 1/100 * 3 = 33.50.
Supriya said:
1 decade ago
I think the correct solution is as follows:
1) consider P=725, R=r, n= 8 months
SI= [725*(8/12)*r]/100= 4.833r
Amount= SI+P
Amount= 4.833r+725
this amount will be principle for next step
2) P= (4.833r+725)+362.5 = 1087.5+4.833r
R= 2r, n=4 months
SI= [ (1087.5+4.883r)*(4/12)*2r]/100 = 33.5
solving this r= 4.529%
Is this solution correct....??
please suggest me..!!
1) consider P=725, R=r, n= 8 months
SI= [725*(8/12)*r]/100= 4.833r
Amount= SI+P
Amount= 4.833r+725
this amount will be principle for next step
2) P= (4.833r+725)+362.5 = 1087.5+4.833r
R= 2r, n=4 months
SI= [ (1087.5+4.883r)*(4/12)*2r]/100 = 33.5
solving this r= 4.529%
Is this solution correct....??
please suggest me..!!
S.Padma said:
7 years ago
Principle=725 r=r% at the beginning of the year so t =1year.
After the 8 months sum of rupees, 362.50 is given additional so the total principle is P=725+362.50=1087.50
t =(12-8)=4 months i.e 4/12 so t=1/3 r=2r.
Rate =(725 * r * 1)/100 + ( 1087.50 * 2r * 1)/100*3 = 33.50
=> 725r +2175r = 33.50 * 100 *3.
=> 2900 r =10050,
=> r=10050/2900,
=> r=3.46%.
After the 8 months sum of rupees, 362.50 is given additional so the total principle is P=725+362.50=1087.50
t =(12-8)=4 months i.e 4/12 so t=1/3 r=2r.
Rate =(725 * r * 1)/100 + ( 1087.50 * 2r * 1)/100*3 = 33.50
=> 725r +2175r = 33.50 * 100 *3.
=> 2900 r =10050,
=> r=10050/2900,
=> r=3.46%.
Aakash said:
1 decade ago
After reading it carefully I got it Tarun.
The rate of interest which is twice in case of 362.50 is twice only for 362.50 and not for (725+ 362.50)/
Second thing ---> don't take this question as a single 1. See both the problems with different view.
Rs 725 is not taken back it is uniform through out the year.
Still any kind of queries are welcomed.
The rate of interest which is twice in case of 362.50 is twice only for 362.50 and not for (725+ 362.50)/
Second thing ---> don't take this question as a single 1. See both the problems with different view.
Rs 725 is not taken back it is uniform through out the year.
Still any kind of queries are welcomed.
Ajay said:
7 years ago
(725*R*8/12)/100 + (725+362.5*2R*4/12)100 = 33.5,
(725*R*8/12)/100 + (1087.5*2R*4/12)/100 = 33.5,
(483.33 R)/100 + (725 R)/100 = 33.50,
(483.33 R) + (725 R) = 33.5*100,
1208.33 R = 3350,
R = 3350/1208.33,
R = 2.772.
(725*2.772*8/12)/100 = 13.398.
(1087.5*5.544*4/12)/100 = 20.097.
By adding, we get 33.495.
(725*R*8/12)/100 + (1087.5*2R*4/12)/100 = 33.5,
(483.33 R)/100 + (725 R)/100 = 33.50,
(483.33 R) + (725 R) = 33.5*100,
1208.33 R = 3350,
R = 3350/1208.33,
R = 2.772.
(725*2.772*8/12)/100 = 13.398.
(1087.5*5.544*4/12)/100 = 20.097.
By adding, we get 33.495.
(2)
Anshul Gupta said:
7 years ago
Initially SI = 725 x R x 2
----------------- ( 8 months = 2/3 year)
3 x 100
= 4.83R.
After 8 months SI = (725+362.5) x 2R x 1.
-------------------------------(remaining 4 months = 1/3 year)
3 x 100.
= 7.25R.
According to Question:
33.5 = 4.83R + 7.25R
33.5 = 12.08R,
R = 33.5/12.08 = 2.77.
Is it right?
----------------- ( 8 months = 2/3 year)
3 x 100
= 4.83R.
After 8 months SI = (725+362.5) x 2R x 1.
-------------------------------(remaining 4 months = 1/3 year)
3 x 100.
= 7.25R.
According to Question:
33.5 = 4.83R + 7.25R
33.5 = 12.08R,
R = 33.5/12.08 = 2.77.
Is it right?
Swapnil said:
8 years ago
In a problem, it is clearly given that, Total amount earned from both loan is 33.50 which is earned at the end of year. It means in a one year.
So as per my solution time for both loan should be 8 months, ie. 8/12 year & 4 months ie. 4/12 year.
But in given solution why the time took 1 year for the first loan. Please explain.
So as per my solution time for both loan should be 8 months, ie. 8/12 year & 4 months ie. 4/12 year.
But in given solution why the time took 1 year for the first loan. Please explain.
Suman said:
1 decade ago
Let the original rate is r%, then new rate is 2r.
here original rate is for only 8 months i.e 2/3; new rate is for 4 month i.e 1/3year(s).
=>{(725*r*2)/(100*3)}+{(362.50*2r*1)/(100*3)}=33.50
=>4.8333333333r+2.4166666667r=33.50
=>7.25r=33.50
=>r=33.50/7.25
=>r=4.6206896552
i.e original rate=4.62%
here original rate is for only 8 months i.e 2/3; new rate is for 4 month i.e 1/3year(s).
=>{(725*r*2)/(100*3)}+{(362.50*2r*1)/(100*3)}=33.50
=>4.8333333333r+2.4166666667r=33.50
=>7.25r=33.50
=>r=33.50/7.25
=>r=4.6206896552
i.e original rate=4.62%
Asad Sodhar said:
7 years ago
Hello guys.
Let me clarify this logic is simple.
The amount 725 is given at rate 'R'.
After 8 months, another amount 362.5 is given at the rate '2R'.
It means 2R is for the amount 362.5, and that too only for 4 months.
While the rate 'R' on 725 would be counted for one whole year. Not just for 8 months.
Let me clarify this logic is simple.
The amount 725 is given at rate 'R'.
After 8 months, another amount 362.5 is given at the rate '2R'.
It means 2R is for the amount 362.5, and that too only for 4 months.
While the rate 'R' on 725 would be counted for one whole year. Not just for 8 months.
SUDHAKAR said:
9 years ago
In my way, the answer is 3.96.
Calculation....
Let orginal rate is =r%
After 8 months=2r%
Then,
The rate of whole one year+rate of after 8 months+rate of other rate=33.5.
725*R*8/12+362.5*2R*4/12+362.5*R*4/12=33.5.
R(725*2+725+362.5)=33.5*300(BECAUSE 1/3*100.
THEN
R=(335*30)/2537.5,
R=3.96.
Calculation....
Let orginal rate is =r%
After 8 months=2r%
Then,
The rate of whole one year+rate of after 8 months+rate of other rate=33.5.
725*R*8/12+362.5*2R*4/12+362.5*R*4/12=33.5.
R(725*2+725+362.5)=33.5*300(BECAUSE 1/3*100.
THEN
R=(335*30)/2537.5,
R=3.96.
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