Aptitude - Simple Interest - Discussion

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.

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.

Hey guys ,

Let the original rate be R%. Then, new rate = (2R)%.

1st,

Rs. 725 is lent in the beginning of the year(Whole year Time =1).

so S.I = 725*R*1/100.

2nd,

After 8 months, a sum of Rs. 362.50 more is lent but at the rate twice the former.

find time,after 8 month means 12-8=4 month remaining.

4 month convert in year = 4/12= 1/3year.

Time = 1/3 year.

and then S.I = 362.50*2R*1/100*3.

Then add each,

(725*R*1/100)+(362.50*2R*1/100*3) = 33.50.

(2175 + 725) R = 33.50 x 100 x 3.

(2175 + 725) R = 10050.

(2900)R = 10050.

R = 10050/2900 = 3.46.

Original rate = 3.46%.

@Rajni.

I thank you for raising the question.

Look here, any interest is calculated, as we generally know at the end of the year. Now you read the problem carefully. The first loan is taken at the beginning of the year, thus the person will be charged the interest for 12 months, but the last one is after 8 months, meaning the person will be charged only 4 months, he has no relation with the previous 8 months, thus here 4 months is our considering fact and you know very well 4 months = 4/12year=1/3year. Thus it's included 1/3year.

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%.

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?

Principle of one year is Rs. 725 and next After 8 months it means a year end with 4 months (8+4=1 year). In this, principle of next 4 months after 8 months be Rs. 362.50.

S.I of 1 year + S.I of after 8 months = Total S.I.

The sum 725 rs has certain interest rate R for 1 year not for 8 months, 8months is just a hint for the next part of the question (12-8=4). They could have simply said for the last 4 months the interest is twice the initial rate for an EXTRA SUM 362.5 rs.

In the question, he gives extra 362.5 sum at the 8th month for twice of R, which does not mean initial sum of 725 Rs it's interest rate is only for 8 months or should be calculated for 8 months.

Look @Maha :).

Let P=principal, I=Interest, R=Rate of Interest, T=time.

Let us consider two loans as Loan1 and Loan2.
In Loan 1: P1=725, R1=x, T1=1year.

In loan 2: P2=362.50 R2=2x, T2=After 8months it means(12-8)4MONTHS i.e., 4/12=1/3YEARS.

Given Interest I=33.50Rs of both Loan1 and Loan2.

Since I=PTR/100.

=>(P1*T1*R1/100)+(P2*T2*R2/100) = I ----EQUATION 1.

Now Insert the values a/c to equation 1 then you will get result.

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.

@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.