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 8 of 10.
Meenakshie said:
1 decade ago
For the 8 month principal should be (725+362.50)=1087.50
Tarun said:
1 decade ago
In question,just after 8 month,,principal change..725 only for 8 month..so its SI should b claculated only for 8 month and thn..for next 4 month the toatal amount(725+362.50) sholud consider as next 4 month principal..at rate 2R..
Shubhra said:
1 decade ago
(725 x R x 1 /100) + (362.50 x 2R x 1 /100 x 3 ) = 33.50
(725 x 1 /100 + 362.50 x 2 /100 x 3) R = 33.50
(725 x 3 + 725 / 100 x 3) R = 33.50
(2175 + 725 ) R = 33.50 x 100 x 3
(2900) R = 10050
R = 10050/2900
R = 3.46%
(725 x 1 /100 + 362.50 x 2 /100 x 3) R = 33.50
(725 x 3 + 725 / 100 x 3) R = 33.50
(2175 + 725 ) R = 33.50 x 100 x 3
(2900) R = 10050
R = 10050/2900
R = 3.46%
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.
GARIMA said:
8 years ago
Why multiplying it with 1/3?
Please explain.
Please explain.
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.
Ujwal said:
9 years ago
The actual expression should be:
(725x2/3xR/100)+(1087.5x1/3x2R/100) = 33.5,
i.e. R=10050/3634 = 2.77%.
(725x2/3xR/100)+(1087.5x1/3x2R/100) = 33.5,
i.e. R=10050/3634 = 2.77%.
Yash said:
9 years ago
Don't consider that the money is being lent to the same person. Take different persons. So it will be different for 8 months and 4 months.
Ray said:
9 years ago
What is 2175 it should also 725, as 362.
50 * 2R *1 becomes 725
50 * 2R *1 becomes 725
Uma said:
9 years ago
725 =p, t = 12m.
pr * 8 + (1/2)p * 2r * 4 = 33.50 * 100.
8pr + 4pr = 3350,
12pr = 3350,
prt = 3350,
725 * r * 1 = 3350,
r = 4.5%.
pr * 8 + (1/2)p * 2r * 4 = 33.50 * 100.
8pr + 4pr = 3350,
12pr = 3350,
prt = 3350,
725 * r * 1 = 3350,
r = 4.5%.
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