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.
M.F.Vinod said:
9 years ago
Hi,
Let me explain everything in clear.
First consider Rs. 725 as principal amount and rate of interest be R% and the time will be 8 months.
Considering PTR = SI.
So we have SI = (725 * 8 * R/100 *12).
After 8 months an amount of Rs. 362.50 added to the principal and the rate to this added amount is 2R% and the time remaining in a year is 4 months.
So for 4 months the rate of interest for the principal amount Rs. 725 remains same as R%.
Total SI = Initial simple interest for 8 months + Added amount simple interest for remaining 4 months + Starting principal amount for remaining 4 months.
Therefore SI = (725 * 8 * R/100 * 12) + (362. 50 * 4 * 2R/100 * 12) + (725 * 4 * R/100 * 12).
SI = (725 * R * 2/100 * 3) + (725 * R/100 * 3) + (725 * R/100 * 3).
SI = (725 * R/100) (2/3 + 1/3 + 1/3).
Therefore, 33. 50= (725 * R/100) (4/3).
(3350 * 3/725 * 4) = R.
R = 3.46551.
Hence, the rate of interest is equal to 3.46551.
Let me explain everything in clear.
First consider Rs. 725 as principal amount and rate of interest be R% and the time will be 8 months.
Considering PTR = SI.
So we have SI = (725 * 8 * R/100 *12).
After 8 months an amount of Rs. 362.50 added to the principal and the rate to this added amount is 2R% and the time remaining in a year is 4 months.
So for 4 months the rate of interest for the principal amount Rs. 725 remains same as R%.
Total SI = Initial simple interest for 8 months + Added amount simple interest for remaining 4 months + Starting principal amount for remaining 4 months.
Therefore SI = (725 * 8 * R/100 * 12) + (362. 50 * 4 * 2R/100 * 12) + (725 * 4 * R/100 * 12).
SI = (725 * R * 2/100 * 3) + (725 * R/100 * 3) + (725 * R/100 * 3).
SI = (725 * R/100) (2/3 + 1/3 + 1/3).
Therefore, 33. 50= (725 * R/100) (4/3).
(3350 * 3/725 * 4) = R.
R = 3.46551.
Hence, the rate of interest is equal to 3.46551.
G K said:
9 years ago
How it comes 2175 + 725 * 3. Where does 3 come from?
Mahesh said:
9 years ago
Cleared with the help of given explanations. Thank you all.
Manjiri said:
9 years ago
Rate of interest is r for 725 and 2r for 362.50;
So, r for 725 for 1 year and 2r for 362.5 for 4 months is correct. The calculations are independent.
So, r for 725 for 1 year and 2r for 362.5 for 4 months is correct. The calculations are independent.
Neha said:
9 years ago
Anybody can explain that why we add 1 year = remaining 4 months. I think it will be 1 year 4 month.
Secondly, after 8 months 362.50 is more.
So we must add 362.50 in 725 for remaining 4 months?
Secondly, after 8 months 362.50 is more.
So we must add 362.50 in 725 for remaining 4 months?
Muneer said:
10 years ago
How it comes 2175?
Kirti said:
10 years ago
Why it has been taken first for 1 year and after 8 years because in the question it has already mention that after 8 years he lended 362.50 and at the beginning he lended 725?
Venu said:
1 decade ago
Hey guys its correct.
Here 725 is given to the person for 1 year. Now you calculate the SI for that, later after 8 months, he again burrows again but the catch is rate is doubled.
Now you know :).
Here 725 is given to the person for 1 year. Now you calculate the SI for that, later after 8 months, he again burrows again but the catch is rate is doubled.
Now you know :).
Agnes said:
1 decade ago
Please why did you multiply 33.50*100*3?
Sonu said:
1 decade ago
Hello sir,
Please let me know the right answer please.
Please let me know the right answer please.
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