23-09-2021 Answers

1. The simple interest on a certain sum for 2 years at 10% per annum is Rs. 90. Find the corresponding compound interest at the same interest rate for 2 years.

Answer: Rs. 94.50

Solution: 90 = P*2*10/100, P = 100 * 90 / (2 * 10) = 450

Amount maturing in 2 years at compound interest = 450 * (1 + 10/100)^2 = 544.50

C.I = Maturing Amount - P = 544.50 - 450 = 94.50

2. A tree increases annually by 1/8th of its height. By how much will it increase after 2 years, if it stands today 64 cms high ?

Answer: 17 cms

Solution: Increase% = (1/8) * 100 = 12.5%

Height after 2 years = 64 * (1 + 12.5/100)^2

= 64 * (1 + 1 / 8 )^2

= 64 * 9/8 * 9/8 = 81cms

Increase in height = 81 - 64 = 17 cms

3. Ashok borrowed some money at 16% simple interest. If he repaid Rs. 10080 in all after 5 years, how much did he borrow ?

Answer: Rs. 5600

Solution: Let the loan amount be x

x + interest for 5 years = 10080

S.I. = 10080 - x

10080 - x = x * 5 * 16 / 100

10080 - x = 4x/ 5, 10080*5 = 9x, x = 5600

4. If the interest on Rs. 1200 be more than the interest on Rs. 1000 by Rs. 50 in 3 years, find the rate of interest.

Answer: 8.33 % approx

Solution: Let rate = R% per annum.

S.I = PNR/100

Then, 1200 * 3 * R / 100 - 1000 * 3 * R / 100 = 50, 6R = 50

R = 8.33 %  approx

5. A sum of money becomes (8/5)th of itself in 5 years at a certain rate of interest. Find the rate of interest  per annum.

Answer: 12%

Solution: Let sum = x, Then, amount = 8x/5

S.I. = 8x/5 - x = 3x/5, 3x/5 = x * 5 * R/100

R = (100 * 3x/5) / (x * 5) = 12%

6. Amir took a loan of Rs. 15000 for 3 years at simple interest. If the total interest paid is Rs. 2700, what is the rate of interest per annum ?

Answer: 6%

Solution: S.I = PNR/100 = 15000 * 3 * R/100 = 2700

R = (2700 * 100 / 15000 * 3) = 6%

7. A principal of Rs. 2600 is lent out in two parts in such a way that the interest on one part at  10% for 5 years is equal to that on another part at 9% for 6 years. Find the amount lent out at 10%.

Answer: Rs.1350

Solution: Let the money lent at 10% be Rs. x. Then the money lent at 9% is Rs. (2600 - x)

x * 5 * 10 / 100 = (2600 - x) * 6 * 9 / 100

x = 2600 * 54 / 104 = 1350

8. The rate of interest for the first 2 years is 5%, for the next 3 years is 8% and beyond this it is 10% per annum. If the simple interest for 8 years is Rs. 1280, what is the principal ?

Answer: Rs. 2000

Solution: 1280 = P*2*5/100 + P*3*8/100 + P*3*10/100

1280 = P * (10 + 24 + 30)/100

Principal = 1280 * 100/64 = 2000

9. In how many years will a sum of money double itself at 12% per annum ?

Answer: 8 years 4 months

Solution: Let principal = P.

Then, S.I. = P, Rate = 12%

P = P * N * 12/100,

N = 100 * P / P * 12 = 25/3 = 8 years 4 months

10. A certain sum of money at simple interest amounts to Rs. 1260 in 2 years and to Rs. 1350 in 5 years. Find the rate of interest per annum.

Answer: 2.5%

Solution: S.I. for 3 years = 1350 - 1260 = 90

S.I for 2 years = (90/3) * 2 = 60

Sum = 1260 - 60 = 1200

S.I (for two years) = 60 = 1200 *  2 * R/100

R = 100 * 60 / 1200 * 2 = 2.5%

11. A man lends Rs. 10000 in four parts. If he gets 8% on Rs.2000, 7.5% on Rs. 4000 and 8.5% on Rs. 1400, what is the rate of interest must he get for the remaining amount if the net interest rate is 8.13% ?

Answer: 9%

Solution: Let R be the rate of interest for the remaining amount

2000 * 1 * 8 / 100 + (4000 * 1 * 7.5/100) + (1400 * 1* 8.5/100) + (2600 * 1 * R/100) = (10000 * 1 * 8.13/100)

16000 + 30000 + 11900 + 2600R = 81300, R = 9%

12. If the simple interest on a certain amount of money be Rs.40 for 2 years and the compound interest on the same amount at the same rate and for the same duration be Rs.45. What is the amount ?

Answer: Rs. 80

Solution: S.I. for 2 years = 40, S.I for 1 year = 20

C.I is more than S.I by the amount of interest obtained in the first year.

Hence 20*R/100  = Diff between C.I and S.I in the second year = 45-40 = 5

So, 20R/100 = 5, R = 25%

Now  considering S.I = PNR/100, 40 = P*2*25/100,

Solving P = 80

13. What is the amount which earns Rs. 132 as compound interest for the second year at 10% per annum ?

Answer: Rs. 1200

Solution: Let P be the principal.

Amount maturing at the end of 1 year = P*(1+10/100) = 1.1P

Amount maturing at the end of 2 years = 1.1P*(1+10/100) = 1.21P

C.I = 1.21P - 1.1P = 0.11P = 132,

P = 132/0.11 = 1200

14. A financier lends Rs. 2000 for 6 months at 20% per annum and the interest is compounded quarterly. Find the amount that he will get after the given period.

Answer: Rs.2205

Solution: A quarter means 3 months. Hence num of quarters in 6 months = 6/3 = 2 = N

As 20% is the annual interest rate, quarterly rate of interest = 20/4 = 5%

Hence, required amount = P (1 + R/100)^N

= 2000 (1 + 5/100)^2 = 2000(21/20)^2 = 2205

15. If A is the simple interest on B and B is the simple interest on C, the rate of interest and the time invested being the same in both cases, what is the relation between A, B and C ?

Answer: B^2 = AC

Solution: S.I = PNR/100

A = B * N * R / 100

B = C * N * R / 100

A/B = B/C, B^2 = AC