Aptitude - Simple Interest - Discussion

11. 

A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is:

[A]. 5%
[B]. 8%
[C]. 12%
[D]. 15%

Answer: Option C

Explanation:

S.I. for 3 years = Rs. (12005 - 9800) = Rs. 2205.

S.I. for 5 years = Rs. 2205 x 5 = Rs. 3675
3

Principal = Rs. (9800 - 3675) = Rs. 6125.

Hence, rate = 100 x 3675 % = 12%
6125 x 5

Video Explanation: https://youtu.be/UYwiBCRN39s


Xyz said: (Jul 18, 2010)  
(2205/3) * 5 ?

Abc said: (Oct 16, 2010)  
@Xyz

For calculationg SI for 1 year we divide it by 3 first and then we want 5yr SI, so we multiplied it by 5 got it.

Acd said: (Feb 11, 2011)  
Principal = Rs. (9800 - 3675) = Rs. 6125 ?

Appu said: (Feb 22, 2011)  
Hai Asd,

In the question we can find "The sum of amount 9800 " it means, principal + SI=9800. So p=9800-SI of 5 years.

I hope u got it.

Akhi said: (Feb 28, 2011)  
Ques: The simple interest of a certain sum for 2 years is Rs 580 and for 5 years is Rs 700 with the same rate of interest. Find the rate of interest.

Can anyone solve this please?

Insaan said: (Mar 7, 2011)  
@ 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

Akhi said: (Mar 10, 2011)  
@Insaan

Actually the question is wrong because it is simple interest while it should be amount. And your solution is correct if it would have been amount.

Krishna said: (Mar 20, 2011)  
Why s.i for 3yrs and 5yrs are taken instead of 5yrs and 8yrs?

Mathan said: (Mar 4, 2012)  
For this type of Question, use this formula.

a = 9800 ; b = 12005 ; t1 = 5 yrs ; t2 = 8 yrs

Principal = (at2 - bt1)/(t2-t1)

Rate = ((b-a)x100)/(bt1-at2) %

Hope it works.

Ruku said: (Apr 30, 2012)  
Thanks madhan, I understand it, thanks lot.

Siva said: (Apr 10, 2013)  
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?

Bhuvana said: (May 20, 2013)  
@Mathan.

Whether this formula works in all those similar problems?

Ravi said: (Sep 2, 2013)  
No @Bhuvana,

Its not working for all, its depend upon the problem all are our mind calculation.

Sruthi said: (Sep 24, 2013)  
Why SI for 3yrs and 5yrs are taken instead of 5yrs and 8yrs?

Zainim said: (Oct 29, 2013)  
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.

Dharshan said: (Jan 28, 2014)  
SI For 3 years = 12500-9800 = 2205.
SI For 1 year = 2205/3 = 735.

So, SI For 5 years = 5*735 = 3675.

Principal for 5 years = 9800-3675 = 6125.
Now calculate rate for 5 years = (3675*100)/(6125*5) = 12%.

Dinesh said: (Jun 11, 2014)  
Why we didn't calculate for 8 yrs?

Kasinath @Hyd said: (Sep 30, 2014)  
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

Amani said: (Oct 25, 2014)  
Why we calculate rate for 5 years?

Vipin Mishra said: (Feb 19, 2015)  
Hi @Kashinath:

In question principle is not mention, Only S.I is mention, that's why All People are taking S.I.

Hemanth said: (Mar 7, 2015)  
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%.

Hemanth said: (Mar 7, 2015)  
In the question given only amount. But when we subtract 8 years amount to 5 years amount we get S.I of 3 years.

Sandu said: (Jul 23, 2015)  
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.

Adarsh said: (Aug 9, 2015)  
A = P+I.

1) 12005 = P+5880 (Total interest for 8 years=5880).

2) P = A-I = 12005-5880 = 6125.

3) SI = PNR/100, 5880 = 6125*8*R/100.

4) So R = 5880*100/8*6125= 12.

Guddu said: (Oct 29, 2015)  
Why difference between amount of two different years is S.I rather than amount?

Siva said: (Jan 10, 2016)  
9800 and 12005 is principle or simple interest? Please explain clearly.

Sandip said: (Feb 27, 2016)  
I = PRT/100 -----> 735 = 6125*R*1/100 ---> R = 12%.

Ramachandran said: (Mar 2, 2016)  
I didn't understand the last step.

Hence, rate = 100 x 3675% = 12%.

6125 x 5.

Anand J said: (Apr 11, 2016)  
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.

Amit said: (May 20, 2016)  
If I want to solve it with 1 years interest i.e. 735 = (6125 * r * 1)/100.

Then the answer is not coming. Why? Someone, please explain.

Shyam said: (Jul 10, 2016)  
THE DIFFERENCE BETWEEN GIVEN YEARS 5 AND 8 IS 3,
SO,

S.I. for 3 years = Rs. (12005 - 9800) = Rs. 2205.
S.I. for 1 year = Rs. (2205/3) = Rs 735.
S.I. for 5 years = 735*5 = Rs. 3675.
Principal = Rs. (9800 - 3675) = Rs. 6125.

Hence, rate = 12%.

Anonymous said: (Sep 15, 2016)  
Can't we think in this way that after five years amount is 9800 and we know each year S.I is 735 and we will add to it but 10% of 9800 is 980. So the answer should be obviously less than 10%. I am talking for the 6th year.

Mani said: (Sep 25, 2016)  
Sir, why you have done (2205/3) * 5?

I didn't understand that step. Please explain me.

Gayatri said: (Oct 7, 2016)  
Not getting this, please explain this sum.

Sanjeev Verma said: (Feb 18, 2017)  
How to solve this after getting SI?

Sankarilakshmi said: (Mar 22, 2017)  
Here,

A1= 9800 and T1 = 5 yrs.
A2=12005 and T2 = 8 yrs.

Formula for this type of question to find R% =( (A1-A2) / (A2*T1 - A1*T2) ) *100.
Therefore,
R% =( (9800 - 12005) / ( 12005*5 - 9800*8 ) ) * 100,
= (-2205 /-18375) * 100,
= 12%.

Mohit Mehta said: (Apr 26, 2017)  
Sum of an amount means? Please, anyone tell me to get it.

Saumendra said: (May 17, 2017)  
12005-9800=2205(SI FOR 3 YEARS).
SI FOR 1 YEAR=2205/3=735.
SI FOR 5 YEARS=735 X 5=3675.
PRINCIPAL 9800-3675=6125.
6125 AMT SI IS 735.
SO,100 AMT SI IS 735/6125 X 100=12%.

Deepak Soni said: (Oct 10, 2017)  
At last,

si=(735*100)/6125,
Si=12%.

Mohanraj said: (Dec 24, 2017)  
SI for 3yrs = 12005-9800=2205.
SI for 1 yr = 2205/3=735.
(SI)Now cal for 5 yrs =735*5=3675.

Principal amt=9800-3675=6125.
SI=PNR/100.
3675=6125*5*R/100.
R=12.

M.L.R.D said: (Jan 10, 2018)  
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.

Rakshith said: (Apr 5, 2018)  
Hi guys,

Can anybody explain me why are we taking (2205/3)*5?

Please.

Sabu said: (May 25, 2018)  
The discussion is very helpful. Thanks.

Aravind Amarnath said: (May 27, 2018)  
(100*3675)/(6125*5)% Please anyone explain this step.

Fera said: (Jun 13, 2018)  
A radio is sold for RM75 cash. Mak minah bought it by making a down payment of RM20. He paid the balance plus interest charged of RM5 after one month. What was the rate was charged?

Can someone help me solve this?

Fera said: (Jun 13, 2018)  
A radio is sold for RM75 cash. Mak Minah bought it by making a down payment of RM20. He paid the balance plus interest charged of RM5 after one month. What was the rate was charged?

Can someone help me to solve this?

Zayia said: (Jun 24, 2018)  
P = SI * 100/(R*T).

Swathi said: (Aug 1, 2018)  
Can anyone explain why they have considered 5 years and not 8 years?

Manju said: (Oct 5, 2018)  
SI for 3 years=12,005-9800=2205.
SI for 1 year=2205/3=735.
SI for 5 year=735*5=3675.
p = total amount - SI.
p = 9800-3675=6125.

The rate of interest = SI *100/p*n,
R = 3675*100/6125*5,
R =12%.

Ramakhil said: (Nov 18, 2018)  
Can any explain why to take 5 years and not 8 years?

Nitishh said: (Jan 7, 2019)  
Nice explanations, Thanks all.

Pramit Shome said: (Mar 12, 2019)  
The answer should be 20%.

Ayaz said: (Apr 8, 2019)  
@Pramit shome.

Would you explain how?

Zaid said: (Apr 9, 2019)  
How will we calculate it with the basic SI formula?

SI = P*T*R/100.

Please explain.

Carlo Ne said: (Apr 25, 2019)  
Thanks all.

Steve said: (Jun 22, 2019)  
How come 3 here?

Mohd Faiq said: (Sep 27, 2019)  
Which formula you have used to find SI for 3 years = (12005-9800)?

Vipul said: (Jan 15, 2020)  
2205=9800*3*R/100.

Is this is correct?

Ays said: (Jan 26, 2020)  
Why do we take 3 year as SI not as amount? Please explain to me.

Annu said: (May 24, 2020)  
In question, it is clearly mentioned that we need to fine rate of interest per annum that is for 1 year but we had find rate of interest for 5 yrs, is it correct.

Kindly explain.

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