### Discussion :: Simple Interest - General Questions (Q.No.11)

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: |
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Answer: Option C Explanation: S.I. for 3 years = Rs. (12005 - 9800) = Rs. 2205.
Principal = Rs. (9800 - 3675) = Rs. 6125.
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. |

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