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.
Nijin said:
4 years ago
Shouldn't we change the number of years as 8/12 and 3/12 instead of 1? Anyone, please clarify.
(18)
Dorji Tshering said:
4 years ago
Hello @Ugyen Dema,
We know S.I = P * R * T.
(725 * R * 1/100) + (362.50*2R*1/100*3)=33.50.
725R/100 + 725R/100*3 = 33.50.
After making same denominator we get,
(2175R/300)+ (725R/300)= 33.50,
(2175R+725R/300)= 33.50,
2900R= 33.50 * 300.
R= 10050/2900.
There by, R= 3.46.
We know S.I = P * R * T.
(725 * R * 1/100) + (362.50*2R*1/100*3)=33.50.
725R/100 + 725R/100*3 = 33.50.
After making same denominator we get,
(2175R/300)+ (725R/300)= 33.50,
(2175R+725R/300)= 33.50,
2900R= 33.50 * 300.
R= 10050/2900.
There by, R= 3.46.
(2)
Dorji Tshering said:
4 years ago
How comes after 8 months = 1/3 months?
I think 12 - 8 = 4, so we have to calculate the interest amount of the second amount for 1/4months.
I think 12 - 8 = 4, so we have to calculate the interest amount of the second amount for 1/4months.
(4)
Ugyen dema said:
4 years ago
How 2175 * 725? Please explain this.
(1)
SIDDHARTH said:
4 years ago
@SOHAM.
NO, we should not take 2/3(YEAR) i.e 8 MONTHS.
BECAUSE the one who have borrowed the money have returned the money only after a year not in the middle i.e is 8 months so we considered it as a year and not as 2/3.
NO, we should not take 2/3(YEAR) i.e 8 MONTHS.
BECAUSE the one who have borrowed the money have returned the money only after a year not in the middle i.e is 8 months so we considered it as a year and not as 2/3.
(6)
Soham said:
4 years ago
P=725 (for 8 months)
rate = R%.
So interest will be;
( 725 * R * 2/3 ) / 100 = 1450R/300.
P=1087.5 (For next 4 months),
Rate = 2R%.
So interest will be;
(1087.5 * 2R * 1/3)/100 = 2175R/300.
So,
(1450R/300 ) + (2175R/ 300 ) = 33.50,
3625R = 10050,
R = 10050/3625.
R = 2.77.
Am I right?
rate = R%.
So interest will be;
( 725 * R * 2/3 ) / 100 = 1450R/300.
P=1087.5 (For next 4 months),
Rate = 2R%.
So interest will be;
(1087.5 * 2R * 1/3)/100 = 2175R/300.
So,
(1450R/300 ) + (2175R/ 300 ) = 33.50,
3625R = 10050,
R = 10050/3625.
R = 2.77.
Am I right?
(6)
Rani said:
4 years ago
Here P= 725 ( For 8 month).
SI= (725 * 8÷12 * r)/100=550r/100
And after 8 month , P= 362.50 more
And p become 725+ 362.50= 1087.50.
Now, SI would be (1087.50 * 2r * 4÷12)/100 =725r/100 ( as the rate of interest double and count for only 4 months).
We have given,(550r+725r)/100 = 33.50
1275r = 3350.
r = 3350/1275 = 2.62 (which is not in the option).
So, the answer is option E- None of these.
SI= (725 * 8÷12 * r)/100=550r/100
And after 8 month , P= 362.50 more
And p become 725+ 362.50= 1087.50.
Now, SI would be (1087.50 * 2r * 4÷12)/100 =725r/100 ( as the rate of interest double and count for only 4 months).
We have given,(550r+725r)/100 = 33.50
1275r = 3350.
r = 3350/1275 = 2.62 (which is not in the option).
So, the answer is option E- None of these.
SEKHAR said:
4 years ago
Why don't we take it like this?
SI = (725 * 8 * R/100 * 2) + (362.50 * 4 * 2R/100 * 2).
SI = (725 * 8 * R/100 * 2) + (362.50 * 4 * 2R/100 * 2).
Nia Sharma said:
5 years ago
I agree @M.F Vinod.
This is the Correct Explanation.
SI is calculated for 8 months and then for the remaining 4 months. 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).
You will get the correct answer.
This is the Correct Explanation.
SI is calculated for 8 months and then for the remaining 4 months. 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).
You will get the correct answer.
Naga dheeraj said:
5 years ago
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%.
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%.
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