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 9 of 10.
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.
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)
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)
Ugyen dema said:
4 years ago
How 2175 * 725? Please explain this.
(1)
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)
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)
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)
Gaurav said:
4 years ago
First amount given was Rs. 725, let the rate be R. A second amount was given i.e. Rs. 362.50 where rate is 2R.
Since it was given after 8 months, and the complete interest of both the amounts was taken together i.e. Rs.33.50.
So, time period for second amount for which the interest will be calculates will be 4 months that is 1/3 year.
Hence,
(725 * R * 1)/100 + (362.50*2R*1/3)/100 = 33.50,
=> 725R/100 + 725R/300 = 33.50,
=> (2175R+ 725R) / 300 = 33.50,
=> 2900R = 33.50*300,
=> R= 3.46%.
Since it was given after 8 months, and the complete interest of both the amounts was taken together i.e. Rs.33.50.
So, time period for second amount for which the interest will be calculates will be 4 months that is 1/3 year.
Hence,
(725 * R * 1)/100 + (362.50*2R*1/3)/100 = 33.50,
=> 725R/100 + 725R/300 = 33.50,
=> (2175R+ 725R) / 300 = 33.50,
=> 2900R = 33.50*300,
=> R= 3.46%.
(24)
Rachana M R said:
4 years ago
@Nijin.
12 months =1 year,
4 months =?
On cross multiplication, we get 4/12 = 1/3.
12 months =1 year,
4 months =?
On cross multiplication, we get 4/12 = 1/3.
(7)
Ab eth said:
3 years ago
Agee @Neha.
Because for 1 year we take 725 principal amount then it says 362.50 more after 8 months, for this reason, it must be 725 + 362.5 for the second principal.
Because for 1 year we take 725 principal amount then it says 362.50 more after 8 months, for this reason, it must be 725 + 362.5 for the second principal.
(26)
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