Aptitude - Simple Interest - Discussion

@All.

Here is the explanation for why you are taking 5 years and not 8 years.

5 years calculation and 8years calculation both the values are same.
S. I for 3 years 12005-9800=2205.
S. I for 1 year= 2205/3=735.
S. I for 5 years=735*5=3675.
S. I for 8 years=735*8=5880
P for 5 years = total amount - s.I => 9800 - 3675 = 6125.
R = si * 100/(p*t)
= 3675 * 100/(6125*5)
= 12%.
P for 8years = 12005 - 5880 = 6125.
R= 5880 * 100/(6125*8),
= 12%.
5years and 8years rate of interest is same.
So take 5 years or 8 years we get the same rate of interest.

We know A = P+SI

As we given,

For 5 years and for 8 years :

= 12500 = P+S.I.

= 9800 = P+S.I------->1.

On subtraction of 8 years and 5 years amount we get S.I of 3 years.

= 12500-9000 = 2205.

Then for S.I of 1 year will become = 735.

Then for 5 years it will become = 5*735 = 3675.

Form (1) we have 9800 = P+S.I.

= 9800-S.I = P.
= 9800-3675 = 6125.
=> P = 6125.

Now we calculate for are for 5 years. As we know S.I for 5 years = 3675.

And P = 6125, and T = 5.

=>3615*100/5*6125.

=>12%.

@ Akhi - the answer of your question is 8%.. its done like the above question here..see

S.I for 3 years (5-2) = 120
S.I for 1 year = 120/3 = 40
hence, S.I for 2 years is 2*40 = 80. (you can also calculate for 5 years instead of 2 years)
Principal = Amount - SI
580 - 80 [amount can also be 700 if we take 5 years]
500
Now, we know SI aswell as Principal
therefore using formula
S.I = PRT/100
80 = 500*R*2/100 [ T can also b 5 if we consider 5 years]
R = 8

We can calculate rate for 5 years or 8 years both give the same answer.

If we calculate S. I for 5 years then we have to calculate rate for 5 years.

See S.I for 5 yrs = 5*735 = 3675.

Then principal for 5 yrs = 9800-3675 = 6125.

Then calculate rate. If we calculate S.I for 8 years then we have to calculate rate for 8 years.

S.I for 8 yrs = 8*735 = 5880.

Then principal for 8 yrs = 12005-5880 = 6125.

Then calculate rate both gives same answer.

Hope it will helpful.

I am not getting a solution for this problem. Then what is the difference between 9800 and 3675 for 5 years. Already we have 9800 for 5 years then why we need 3675?

I tried like the bellow method.
for 1 year:
P x 1 x R/100

for 5 years:
9800 = P x 5 x R/100.

for 8 years:
12005 = P x 8 x R/100.
But I did not get answer after seeing the explanation. Please explain.

Step 1 : Earned simple interest in last 3 year = 12005 - 9800 = 2205.
Step 2 : Earned interest per year = 2205 ÷ 3 = 735.
Step 3 : Since Simple Interest earned per year is 735 hence the sum of Simple Interest for initial 5 years will be;
735 x 5 = 3675.
Step 4: So the Principle amount will be 9800 - 3675 = 6125.
Step 5 : Now use S.I. formula for calculating R%.

Amount = P+I for 5 years = 9800 --- Eq(1).

Amount = P+I for 8 years =12005 -- Eq(2).

Eq(2)-Eq(1) => Amount = 735 for 3yrs.

Amount = P+I per year = 2205/3 = 735.

Therefore data is Inadequate to find Rate of interest.

But why Everyone took 9800 as SI sometimes and as principal sometimes. please help

In first step >>> S.I. for 3 years = Rs. (12005 - 9800) = Rs. 2205.

How come it is S.I = 2205?. It should be difference in SI + Principal for 3 years = 2205. How come it is SI alone?

12005 is SI + Principal for 5yrs and 9800 is also SI + Prncpl for 8 yrs.

please someone explain?

After 5 years,
P + S.I = 9800 (sum of money amount).

After 8 years,
P + S.I = 12005 (sum of money amount).

P is no change. But S.I change every year. Therefore the sum of money amount will be changed. That's why the difference of the sum of money amount is equal to different of S.I.

In first step >>> S.I. for 3 years = Rs. (12005 - 9800) = Rs. 2205.

How come it is S.I = 2205?. It should be difference in SI + Principal for 3 years = 2205. How come it is SI alone?

12005 is SI + Principal for 5 years and 9800 is also SI + Principle for 8 years.