Simple Interest | Set-2

23 Jun, 2021
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 + tn-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 
singh_teekam
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