Simple Interest | Set-2

Question 1: A sum of money becomes 6/5 of itself in 3 years at a certain rate of simple interest. The rate of interest per annum is 
Solution: Let principal = 5P 
Hence amount = 5P x 6P/5 = 6P 
SI= 6P – 5P = P 
Time = 3 years 
SI = P x R x T/100 
P = 5P x R x 3 / 100 
R = 100/15 
R = 6.66 % 

Question 2: The simple interest on a certain sum at 6% per annum for 4 years and 5 years differs by Rs 60. The sum is 
Solution: Note : The simple interest for every year will be same. 
SI in 4 years = 4 x 6 = 24% 
Si in 5 years = 5 x 6 = 30% 
Difference in interest = 30 – 24 = 6% 
Acc. to question 
6% -> 60 
1% -> 10 
100% -> 1000

Question 3: What amount of money will amount to 750 in 6 years and to 800 in 8 years at simple interest? 
Solution: 

 Amount             Time
 750                 6
  |                  |+2   
 800                 8

Hence interest in 2 years = Rs 50 
Interest in 1 year = 25 
Interest in 6 year = 25 x 6 =150 
Principal = Amount – SI 
= 750 – 150 = Rs 600 

Question 4: If Rs 64 amount to 83.20 in 2 years what will Rs 150 amount to in 4 years at the same rate percent per annum? 
Solution: Let the rate of interest = R% 
Interest in 2 years = 83.20 – 64 = 19.20 
R% = SI x 100 / P x T 
R% = 19.20 x 100 / 64 x 2 
R% = 30/2 = 15% 
Therefore amount of 150 in 4 years at rate 15% 
SI = 150 x 15 x 4/ 100 
=90 
Amount = P + SI 
= 150 + 90 
=Rs 240

Question 5: A person invest money in three different schemes for 6 years, 10 years and 12 years at 10%, 18% and 30% simple interest respectively. At the completion of each scheme, he gets the same interest. The ratio of his investment is 
Solution: When interest is equal then sum of amount will be distributed in following ratio. 
1/R₁ T₁ : 1/R₂ T₂ : 1/R₃ T₃
1/6×10 : 1/10×18 : 1/12×30 
1/6 : 1/18 : 1/36 
6 : 2 : 1

Question 6: Simple interest on Rs 1000 for 2 years at 7.5% per annum is equal to the simple interest on Rs 800 at 3.75% per annum for a certain period of time. The period of time 
Solution: Let the period of time = t 
Acc. to question 
1000 x 2 x 7.5/ 100 = 800 x 3.75 x t / 100 
40/8 = t 
t = 5 
Hence, the time period 5 years

Question 7: With the given rate of simple interest, the ratio of principal and amount for a certain 
period of time 4:5. After 3 years, with the same rate of interest, the ratio of the principal and amount becomes 5:7. The rate of interest is 
Solution: 

Principal        Amount         Interest
   4x5            5x5             1x5
   5x4            7x4             2x4
Principal will be same so equate the principal.
Principal        Amount         Interest
  20              25              5
  20              28              8

Interest in 3 years = 3 units 
Required rate= 1/20 x 100 = 5%

Question 8: What equal installment of annual payment will dis-charge a debt which is due as Rs 848 at the end of 4 years at 4% per annum simple interest? 
Solution: Value of installment = Principal x 100/( time x 100 + t_n-1…….1 x Rate% ) 
Principal = 848 
Rate =4% 
Formula= Due Debt x 100 / 100 x t + r x [t(t-1)/2]
Installment = 848 x 100 / [100 x 4 + 4 x (4 x 3)/2]
= (848 x 100) / 424
= Rs 200

Question 9: Rs 2000 is invested at a rate of 6% per annum on Simple interest. If after every 10 year interest is added in the principal then find in how much time the sum amounts to Rs 4000. 
Solution: In first 10 year at rate 6% 
Amount = (2000 x 6 x 10) / 100 
= 1200 
After 10 years interest added in the principal
New principal= 2000 + 1200 = 3200 
Simple Interest for next y years = 4000 – 3200 = 800 
800 = (3200 x 6 x y) / 100 
y = 100/24 
It will take time 4 year 2 month. 
Hence, Total time taken = 10 year + 4 year 2 month = 14 year 2 month

Question 10: Simple Interest on certain sum of money of 10 year is 3130 but if after 5 year principal become 5 times then find the total SI after 10 years. 
Solution. SI of 10 years = 3130 
Simple Interest same in every year. 
So, SI in first 5 year = (3130/10)*5 = 1565 
If principal become 5 times in 5 year than interest will also become 5 times. 
So, Interest of next 5 years= 1565 x 5 = 7825 
Total Simple Interest = 7825 + 1565 = 9390