**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/R _{1} T_{1} : 1/R_{2} T_{2} : 1/R_{3} T_{3} **

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 4_{x5}5_{x5}1_{x5}5_{x4}7_{x4}2_{x4}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**