Problems on Simple Interest
Q1. At which sum, the simple interest at the rate of 3¼ per annum will be Rs. 210 in 2½ years.
(a) 2311.25
(b) 2355.30
(c) 2584.60
(d) 2716.90
Answer: (c) 2584.60
P = ? r = 3¼ % = 13/4%; S.I = 210 t = 2½y = 5/2 y
P = | S.I X 100 |
r X t |
= | 210 X 100 | = | 210 X 100 X 8 | = Rs. 2584.60 |
(13/4) X (5/2) | 13 X 5 |
Q2. A sum of money amount to Rs. 4200 in 4 years and to Rs. 4680 in 7 years at simple interest. The rate of interest per annum is
(a) 3312
(b) 3560
(c) 3590
(d) 3626
Answer: (b) 3560
S.I for 3 years = Rs (4680 - 4200) = Rs. 480
∴ S.I for 1 year = Rs. (480/3) = Rs. 160
∴ S.I for 4 years = Rs. 160 X 4 = Rs. 640
Principal (P) = Rs. (4200 - 640) = Rs. 3560
∴ r = | 100 X S.I | = | 100 X 640 % | = 4.49 % |
p X t | 3560 X 4 |
Q3. How much simple interest will Rs. 3000 earn in 18 months at 5% per annum
(a) 225
(b) 250
(c) 262
(d) 310
Answer: (a) 225
S.I = | P X r X t | = | 3000 X (18/12) X 5 | = | 3000 X 18 X 5 | = 225 |
100 | 100 | 100 X 12 |
Q4. A man deposited Rs. 300 for 2 years, Rs. 600 for 4 years and Rs. 1200 for 6 years. He received Rs. 1020 as the simple interest. The rate of interest per annum is
(a) 10 %
(b) 15 %
(c) 20 %
(d) 30 %
Answer: (a) 10 %
Let the rate of interest be r %
A/Q | 300 X r X 2 | + | 600 X r X 4 | + | 1200 X r X 6 | = 1020 |
100 | 100 | 100 |
⇒ | 600r | + | 2400r | + | 7200r | = 1020 |
100 | 100 | 100 |
⇒ 600r + 2400r + 7200r = 102000
⇒ 10200r = 102000
⇒ r = 10
∴ r = 10 %
Q5. Simple interest on Rs. 600 for 4 years at 5.25% per annum is equal to the simple interest on 400 at 5% per annum for a certain period of time. The time period is ?
(a) 5 years
(b) 5.5 years
(c) 6.3 years
(d) 7.2 years
Answer: (c) 6.3 years
A/Q S.I for 4 years = S.I for t years
⇒ | 600 X 5.25 X 4 | = | 400 X 5 X t |
100 | 100 |
⇒ t | = | 600 X 5.25 X 4 | = | 31.5 | = 6.3 years |
400 X 5 | 5 |
Q6. A borrows Rs. 800 at the rate of 12% per annum simple interest and B borrows Rs. 910 at the rate of 10% per annum simple interest. In how many years will their amount of debts be equal ?
(a) 8 years
(b) 13 years
(c) 19 years
(d) 22 years
Answer: (d) 22 years
Let the required time be t years
Now 800 + | 800 X 12 X t | = 910 + | 910 X 10 X t |
100 | 100 |
⇒ 96t - 91t = 910 - 800
⇒ 5t = 110
⇒ t = 22
Q7. Rs. 5000 becomes Rs. 6200 in 4 years at a certain rate of interest. If the rate becomes 1.5 times of itself, the amount of the same principal in 5 years will be
(a) 5536
(b) 5996
(c) 6886
(d) 7250
Answer: (d) 7250
S.I for 4 years = Rs. (6200 - 5000) = Rs. 1200
S.I for 1 years = Rs. (1200/4) = Rs. 300
∴ Rate of Interest = | S.I X 100 | = | 1200 X 100 | = 6% |
P X t | 5000 X 4 |
Now Rate = 6 X 1.5% = 9%
∴ Required amount = 5000 + | 5000 X 9 X 5 | = Rs. (5000 + 2250) | =Rs. 7250 |
100 |
Q8. If the simple interest for 5 years be equal to 25% of the principal, it will be equal to the principal after
(a) 10 years
(b) 20 years
(c) 30 years
(d) 40 years
Answer: (b) 20 years
Let the principal be P and rate be r
A/Q | P X r X 5 | = P X 25% |
100 |
⇒ | p X r X 5 | = P X | 25 |
100 | 100 |
⇒ r = | 25 | X | 100 | = 5% |
100 | 5 |
Let the required time be t years
P X r X t | = P |
100 |
⇒ | P X 5 X t | = P |
100 |
⇒ t = | 100 | = 20 years |
5 |
Q9. Hari took a loan at simple interest at 6% in the first year with an increase of 0.5% in each subsequent year. He paid Rs. 3375 as interest after 4 years. How much loan did he take ?
(a) 10950
(b) 11750
(c) 12500
(d) 12700
Answer: (c) 12500
Now x X | 6 | X 1 + x X | 6.5 | X 1 + x X | 7 | X 1 + x X | 7.5 | X 1 = 3375 |
100 | 100 | 100 | 100 |
⇒ (6 + 6.5 + 7 + 7.5) X (x/100) = 3375
⇒ x = 3375 X (100/27) = 12500
Q10. At what rate of simple interest a certain sum will be doubled in 14 years
(a) 7 | 1 | years |
7 |
(b) 7 | 1 | years |
9 |
(c) 8 | 1 | years |
5 |
(d) 9 | 1 | years |
3 |
Answer:
(a) 7 | 1 | years |
7 |
Let the sum be Rs. x
Here P = Rs. x
A = Rs. 2 X x = Rs. 2x
S.I = A - P = 2x -x = Rs. x
t = 14 years
r = ?
Now r = | S.I X 100 | = | x X 100 | = | 50 | = 7 | 1 | years |
P X t | x X 14 | 7 | 7 |
Practice Test Exam