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 7 of 10.
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.
Kajal singh said:
8 years ago
Thank you everyone for explaining it.
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.
Raj said:
7 years ago
Either this solution is wrong or question statements are misleading.
1. It says after 8 months, 362.50 MORE is lent so it seems it will become 725+362.50.
2. And total interest is of a year then first interest should be on first 8 months and next interest of 4 months?
1. It says after 8 months, 362.50 MORE is lent so it seems it will become 725+362.50.
2. And total interest is of a year then first interest should be on first 8 months and next interest of 4 months?
Shantanil Hazarika said:
7 years ago
@ALL.
Here, it isn't clearly stated that that 33.50 is collected as all together form both the loans.
So, how to get the answer? Please tell me.
Here, it isn't clearly stated that that 33.50 is collected as all together form both the loans.
So, how to get the answer? Please tell me.
SHUBHaM SaKHaRE said:
7 years ago
725*(8/12)*r + (725+362.5)*(4/12)*2r = 33.5*100.
Hence;
r=2.77%.
Hence;
r=2.77%.
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?
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%.
Shibat sunwar said:
7 years ago
The Ans is 2.31.
Second principle is 725+362.5.
Second principle is 725+362.5.
Shibat said:
7 years ago
@S Padma.
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.
=> 725*3r +2175r = 33.50 * 100 *3.
=> 43500 r =10050,
=> r=10050/4350,
=> r=2.31.
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.
=> 725*3r +2175r = 33.50 * 100 *3.
=> 43500 r =10050,
=> r=10050/4350,
=> r=2.31.
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