SIMPLE INTEREST

Practice Questions

Q1. A sum of money becomes 7/4 of itself in 6 years at a certain rate of simple interest. What is the annual rate of interest?

(A) 10%
(B) 12.5%
(C) 15%
(D) 16%

Solution:
Let the principal be P.
Amount = (7/4)P
Simple Interest (SI) = Amount − Principal
SI = (7/4)P − P = (3/4)P
Using the formula:
SI = (P × R × T) / 100
(3/4)P = (P × R × 6) / 100
3/4 = 6R / 100
6R = 75
R = 75 / 6 = 12.5%
Therefore, the annual rate of interest is 12.5% (B)

Q2. A man lent out a certain sum at 10% per annum simple interest. In 5 years, the interest amounted to Rs360 less than the sum lent. Find the sum lent.

(A) Rs820
(B) Rs150
(C) Rs720
(D) Rs200

Solution:
Let the principal be P.
Rate (R) = 10% per annum
Time (T) = 5 years
SI = (P × R × T) / 100
SI = (P × 10 × 5) / 100
SI = P/2
According to the question:
P − SI = 360
P − P/2 = 360
P/2 = 360
P = 360 × 2 = Rs720
Therefore, the sum lent was Rs720 (C)

Q3. At what rate per annum simple interest will a principal of Rs. 5,000 amounts to Rs. 6,200 in 3 years?

(A) 6%
(B) 8%
(C) 10%
(D) 12%

Solution:
Principal (P) = Rs. 5,000
Amount (A) = Rs. 6,200
Time (T) = 3 years
Interest (SI) = 6200 − 5000 = Rs. 1,200
Rate = (1200 × 100) / (3 × 5000) = 8%
Correct Option: (B)

Q4. A sum was put at simple interest at a certain rate for 3 years. Had it been put at a 2% higher rate, it would have fetched Rs 120 more. Find the sum.

(A) Rs1,500
(B) Rs1,800
(C) Rs2,000
(D) Rs2,400

Solution:
An increase of 2% per annum for 3 years gives an additional interest of:
Additional interest = 2% × 3 = 6%
Let the principal be P.
6% of P = 120
(6/100) × P = 120
P = (120 × 100) / 6
P = Rs2,000
Therefore, the sum is Rs 2,000 (C)

Q5. Find the simple interest on Rs2,500 at 8% per annum for 3 years.

(A) Rs500
(B) Rs550
(C) Rs600
(D) Rs650

Solution:
Given,
Principal (P) = Rs2,500
Rate (R) = 8% per annum
Time (T) = 3 years
Using the formula:
SI = (P × R × T) / 100
SI = (2,500 × 8 × 3) / 100
SI = 60,000 / 100
SI = Rs600
Therefore, the simple interest is Rs600 (C)

Q6. A sum of Rs 4,000 earns simple interest at 5% per annum for 4 years. Find the total amount.

(A) Rs4,600
(B) Rs4,700
(C) Rs4,800
(D) Rs5,000

Solution:
Given,
Principal (P) = Rs4,000
Rate (R) = 5% per annum
Time (T) = 4 years
Using the formula:
SI = (P × R × T) / 100
SI = (4,000 × 5 × 4) / 100
SI = Rs800
Amount = Principal + Simple Interest
Amount = 4,000 + 800
Amount = Rs4,800
Therefore, the total amount is Rs4,800 (C)

Q7. At what rate per annum will Rs 3,000 earn simple interest of Rs 900 in 5 years?

(A) 4%
(B) 5%
(C) 6%
(D) 8%

Solution:
Given,
Principal (P) = Rs 3,000
Simple Interest (SI) = Rs 900
Time (T) = 5 years
Using the formula:
SI = (P × R × T) / 100
900 = (3,000 × R × 5) / 100
900 = 150R
R = 900 / 150
R = 6%
Therefore, the annual rate of interest is 6% (C)

Q8. In how many years will Rs 2,000 earn simple interest of Rs 600 at 5% per annum?

(A) 4 years
(B) 5 years
(C) 6 years
(D) 8 years

Solution:
Given,
Principal (P) = Rs 2,000
Simple Interest (SI) = Rs 600
Rate (R) = 5% per annum
Using the formula:
SI = (P × R × T) / 100
600 = (2,000 × 5 × T) / 100
600 = 100T
T = 600 / 100
T = 6 years
Therefore, the required time is 6 years (C)

Q9. A sum of money amounts to Rs 3,600 in 4 years at 5% per annum simple interest. Find the principal.

(A) Rs 2,800
(B) Rs 3,000
(C) Rs 3,200
(D) Rs 3,400

Solution:
Let the principal be P.
Given,
Amount (A) = Rs 3,600
Rate (R) = 5% per annum
Time (T) = 4 years
Amount = Principal + Simple Interest
A = P + (P × R × T) / 100
3,600 = P + (P × 5 × 4) / 100
3,600 = P + P/5
3,600 = 6P/5
P = (3,600 × 5) / 6
P = Rs 3,000
Therefore, the principal is Rs 3,000 (B)

Q10. The simple interest on a sum of money at 6% per annum for 4 years is Rs 720. Find the principal.

(A) Rs 2,500
(B) Rs 2,800
(C) Rs 3,000
(D) Rs 3,200

Solution:
Given,
Simple Interest (SI) = Rs 720
Rate (R) = 6% per annum
Time (T) = 4 years
Let the principal be P.
Using the formula:
SI = (P × R × T) / 100
720 = (P × 6 × 4) / 100
720 = 24P / 100
P = (720 × 100) / 24
P = Rs 3,000
Therefore, the principal is Rs 3,000 (C)

Q11. A sum of Rs 5,000 is invested at 7% per annum simple interest for 2 years. Find the amount at the end of 2 years.

(A) Rs 5,500
(B) Rs 5,600
(C) Rs 5,700
(D) Rs 5,800

Solution:
Given,
Principal (P) = Rs 5,000
Rate (R) = 7% per annum
Time (T) = 2 years
Using the formula:
SI = (P × R × T) / 100
SI = (5,000 × 7 × 2) / 100
SI = Rs 700
Amount = Principal + Simple Interest
Amount = 5,000 + 700
Amount = Rs 5,700
Therefore, the amount is Rs 5,700 (C)

Q12. The simple interest on a certain sum at 8% per annum for 5 years is Rs 1,200. Find the sum.

(A) Rs 2,500
(B) Rs 3,000
(C) Rs 3,500
(D) Rs 4,000

Solution:
Given,
Simple Interest (SI) = Rs 1,200
Rate (R) = 8% per annum
Time (T) = 5 years
Let the principal be P.
Using the formula:
SI = (P × R × T) / 100
1,200 = (P × 8 × 5) / 100
1,200 = 40P / 100
P = (1,200 × 100) / 40
P = Rs 3,000
Therefore, the sum is Rs 3,000 (B)

Q13. A sum of Rs 2,400 amounts to Rs 3,120 in 5 years at simple interest. Find the annual rate of interest.

(A) 4%
(B) 5%
(C) 6%
(D) 8%

Solution:
Given,
Principal (P) = Rs 2,400
Amount (A) = Rs 3,120
Time (T) = 5 years
Simple Interest = Amount − Principal
SI = 3,120 − 2,400
SI = Rs 720
Using the formula:
SI = (P × R × T) / 100
720 = (2,400 × R × 5) / 100
720 = 120R
R = 720 / 120
R = 6%
Therefore, the annual rate of interest is 6% (C)

Q14. A sum of money doubles itself in 10 years at simple interest. Find the annual rate of interest.

(A) 5%
(B) 8%
(C) 10%
(D) 12%

Solution:
Let the principal be P.
Since the sum doubles itself,
Amount = 2P
Simple Interest = Amount − Principal
SI = 2P − P
SI = P
Given, Time (T) = 10 years
Using the formula:
SI = (P × R × T) / 100
P = (P × R × 10) / 100
Cancelling P from both sides:
1 = 10R / 100
100 = 10R
R = 10%
Therefore, the annual rate of interest is 10% (C)

Q15. A sum of Rs 6,000 is lent at 9% per annum simple interest. Find the interest earned in 2 years and 6 months.

(A) Rs 1,200
(B) Rs 1,250
(C) Rs 1,350
(D) Rs 1,500

Solution:
Given,
Principal (P) = Rs 6,000
Rate (R) = 9% per annum
Time (T) = 2 years and 6 months
T = 2.5 years
Using the formula:
SI = (P × R × T) / 100
SI = (6,000 × 9 × 2.5) / 100
SI = 135,000 / 100
SI = Rs 1,350
Therefore, the simple interest is Rs 1,350 (C)