Aptitude - Simple Interest - Discussion

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.

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%.

It is not specified in the the question.

1. What is original rate of interest whether it is rate of all the money involved or it is only for money other than 362.50 rupees?

after 8 months principle should be 725+362.50 but in answer he was write only 362.50 how will it come?

And original rate only 8 months so time=8/12 years but he was write 1 year. how is?

In question there is written After 8 months the rate is twice.

Then, why in the answer this is written the new rate (twice) is only for 4 months.

In the question the SI for the second loan should be calculated for 4 months and not the whole year.

Hi,

In this question,for 8 months 750 with r%,remaining 362.5 with 2r% but he is doing for 1 year & 4 months,may be the answer is wrong ? what he explained.

Here, original rate is for 1 year (s) ; the new rate is for only 4 months i.e. 1/3year (s).
Can anybody explain this line. How it becomes 1/3 ?

Suman answer is wrong. Because in question he lent the amt and doesnt paid it back. If he pays after 8 months we can consider it as 8/12. Explanation given to the answer is correct.

The interest of Rs725 he had collect at the end of the year with the interest of 4 months of Rs 362.5 so calculate it &you will get the correct answer.