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 + tn-1…….1 x Rate% )
Principal = 848
Rate =4%
Formula= Due Debt x 100 / 100 x t + r x [t(t-1)/2]
Installment = 4200 x 100 / 100 x 5 + (10 x 5 x 4) / 2
= 4200 x 100 / (500 + 100)
= Rs 700

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



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