Question 1

Two sums of money are in the ratio 3:4. If they are invested at 5% simple interest per annum for 2 years, the difference in their interests will be ₹200. What is the larger sum?

Accepted Answer

Step 1: Let the sums be 3x and 4x. Step 2: SI on 3x = (3x × 5 × 2) / 100 = 0.3x. SI on 4x = (4x × 5 × 2) / 100 = 0.4x. Step 3: Difference in SI = 0.4x - 0.3x = 0.1x = 200. Step 4: x = 2000. Step 5: Larger sum = 4x = 4 × 2000 = ₹8,000.

Question 2

A sum of ₹5,000 is invested at a simple interest rate of 8% per annum. What will be the interest earned after 3 years?

Accepted Answer

Step 1: Use the Simple Interest formula: SI = (P × R × T) / 100. Step 2: Substitute values: SI = (5000 × 8 × 3) / 100 = 120000 / 100 = ₹1,200. Therefore, the interest earned is ₹1,200.

Question 3

Rajesh borrowed ₹12,000 at 5% simple interest per annum. How much total amount will he repay after 4 years?

Accepted Answer

Step 1: Calculate Simple Interest using SI = (P × R × T) / 100 = (12000 × 5 × 4) / 100 = 2400. Step 2: Total Amount = Principal + SI = 12000 + 2400 = ₹14,400. Therefore, Rajesh will repay ₹14,400.

Question 4

At what rate of simple interest per annum will ₹8,000 become ₹9,600 in 2 years?

Accepted Answer

Step 1: Calculate SI = Amount - Principal = 9600 - 8000 = ₹1,600. Step 2: Use SI = (P × R × T) / 100, so 1600 = (8000 × R × 2) / 100. Step 3: 1600 = 160R, therefore R = 10% per annum.

Question 5

A principal amount becomes ₹6,500 in 5 years at 6% simple interest per annum. What was the original principal?

Accepted Answer

Step 1: Let Principal = P. Amount = P + SI, where SI = (P × 6 × 5) / 100 = 30P / 100 = 0.3P. Step 2: 6500 = P + 0.3P = 1.3P. Step 3: P = 6500 / 1.3 = ₹5,000. Therefore, the original principal was ₹5,000.

Question 6

In how many years will ₹3,000 earn ₹900 as simple interest at 6% per annum?

Accepted Answer

Step 1: Use SI = (P × R × T) / 100. Step 2: Substitute: 900 = (3000 × 6 × T) / 100. Step 3: 900 = 180T. Step 4: T = 900 / 180 = 5 years. Therefore, it will take 5 years.

Question 7

A man borrowed ₹12,000 at 9% per annum simple interest. He repaid ₹4,000 after 2 years. How much will he owe after another 3 years if no further repayment is made?

Accepted Answer

Step 1: SI for first 2 years on ₹12,000 = (12000 × 9 × 2) / 100 = ₹2,160. Step 2: Amount after 2 years = 12000 + 2160 = ₹14,160. Step 3: After repaying ₹4,000, remaining principal = 14160 - 4000 = ₹10,160. Step 4: SI for next 3 years on ₹10,160 = (10160 × 9 × 3) / 100 = ₹2,743.20 ≈ ₹2,743. Step 5: Total amount owed = 10160 + 2743 = ₹12,903.

Question 8

A sum of ₹8,000 is invested at 12% per annum simple interest. How much interest will be earned in 3 years and 6 months?

Accepted Answer

Step 1: Identify SI formula: SI = (P × R × T) / 100. Step 2: Convert time to years: 3 years 6 months = 3.5 years. Step 3: SI = (8000 × 12 × 3.5) / 100 = (8000 × 42) / 100 = 336000 / 100 = ₹3,360.

Question 9

At what rate per annum will ₹5,000 amount to ₹6,500 in 5 years under simple interest?

Accepted Answer

Step 1: SI = Amount - Principal = 6500 - 5000 = ₹1,500. Step 2: Use SI = (P × R × T) / 100. Step 3: 1500 = (5000 × R × 5) / 100. Step 4: 1500 = 250R. Step 5: R = 1500 / 250 = 6% per annum.

Question 10

Two sums of money are in the ratio 3:5. If they are invested at 10% per annum simple interest for 2 years, the difference in their interests will be ₹600. What are the two sums?

Accepted Answer

Step 1: Let the two sums be 3x and 5x. Step 2: SI on first sum = (3x × 10 × 2) / 100 = 0.6x. Step 3: SI on second sum = (5x × 10 × 2) / 100 = x. Step 4: Difference in SI = x - 0.6x = 0.4x = 600. Step 5: x = 1500. Step 6: First sum = 3 × 1500 = ₹4,500. Second sum = 5 × 1500 = ₹7,500.

Question 11

A sum of ₹6,400 is lent at a simple interest rate of 12.5% per annum. In how many years will the interest amount to ₹2,400?

Accepted Answer

Step 1: Use SI formula — SI = (P × R × T) / 100. Step 2: 2400 = (6400 × 12.5 × T) / 100. Step 3: 2400 = 800 × T. Step 4: T = 2400 / 800 = 3 years. Therefore, the answer is 3 years.

Question 12

The simple interest on ₹6,000 at 7% per annum for a certain period is ₹840. What is the principal amount that would earn the same interest in 2 years at 6% per annum?

Accepted Answer

Step 1: Find the time period from the first scenario using SI = (P × R × T) / 100: 840 = (6000 × 7 × T) / 100, so T = 840 × 100 / (6000 × 7) = 84000 / 42000 = 2 years. Step 2: Now find the principal for the second scenario using the same formula rearranged: P = (SI × 100) / (R × T) = (840 × 100) / (6 × 2) = 84000 / 12 = ₹7,000. Therefore, the required principal is ₹7,000.

Question 13

A sum of ₹5,000 is invested at a simple interest rate of 8% per annum. What will be the interest earned after 3 years?

Accepted Answer

Step 1: Use the simple interest formula: SI = (P × R × T) / 100. Step 2: Substitute values: SI = (5000 × 8 × 3) / 100 = 120000 / 100 = ₹1,200. Therefore, the interest earned is ₹1,200.

Question 14

If ₹8,000 amounts to ₹9,600 in 2 years at simple interest, what is the rate of interest per annum?

Accepted Answer

Step 1: Calculate simple interest: SI = Amount - Principal = 9600 - 8000 = ₹1,600. Step 2: Use SI = (P × R × T) / 100 to find R. Step 3: 1600 = (8000 × R × 2) / 100. Step 4: 1600 = 160R, so R = 10% per annum.

Question 15

A principal of ₹12,000 is invested at 5% per annum simple interest. How many years will it take for the amount to become ₹15,000?

Accepted Answer

Step 1: Calculate simple interest: SI = Amount - Principal = 15000 - 12000 = ₹3,000. Step 2: Use SI = (P × R × T) / 100 to find T. Step 3: 3000 = (12000 × 5 × T) / 100. Step 4: 3000 = 600T, so T = 5 years.

Question 16

A sum of ₹8,000 earns ₹1,600 as simple interest in 4 years. What is the rate of interest per annum?

Accepted Answer

Step 1: Use SI = (P × R × T) / 100 and rearrange for R: R = (SI × 100) / (P × T). Step 2: Substitute values: R = (1600 × 100) / (8000 × 4) = 160000 / 32000 = 5% per annum. Therefore, the rate is 5% per annum.

Question 17

A sum becomes ₹7,200 in 4 years at 10% per annum simple interest. What was the original principal?

Accepted Answer

Step 1: Let principal be P. Using Amount = P + SI and SI = (P × R × T) / 100. Step 2: 7200 = P + (P × 10 × 4) / 100. Step 3: 7200 = P + 0.4P = 1.4P. Step 4: P = 7200 / 1.4 = ₹5,000.

Question 18

Two friends invested money at simple interest. Priya invested ₹10,000 at 8% per annum for 2 years, while Arun invested ₹8,000 at 10% per annum for 2 years. Who earned more interest and by how much?

Accepted Answer

Step 1: Calculate Priya's interest: SI = (10000 × 8 × 2) / 100 = ₹1,600. Step 2: Calculate Arun's interest: SI = (8000 × 10 × 2) / 100 = ₹1,600. Step 3: Both earned equal interest. The difference is ₹0.

Question 19

Rajesh deposits ₹5,000 in a bank at a simple interest rate of 8% per annum. How much interest will he earn after 3 years?

Accepted Answer

Step 1: Use the simple interest formula: SI = (P × R × T) / 100. Step 2: Substitute values: SI = (5000 × 8 × 3) / 100 = 120000 / 100 = ₹1,200. Therefore, the interest earned is ₹1,200.

Question 20

Priya borrowed ₹12,000 at 5% simple interest per annum. After how many years will the interest amount to ₹3,000?

Accepted Answer

Step 1: Use SI = (P × R × T) / 100 and rearrange for T: T = (SI × 100) / (P × R). Step 2: Substitute values: T = (3000 × 100) / (12000 × 5) = 300000 / 60000 = 5 years. Therefore, the time period is 5 years.

Question 21

Rajesh borrowed ₹20,000 at 6% per annum simple interest. If he paid ₹23,600 to clear the debt, for how many years did he borrow the money?

Accepted Answer

Step 1: Calculate simple interest: SI = 23600 - 20000 = ₹3,600. Step 2: Use SI = (P × R × T) / 100. Step 3: 3600 = (20000 × 6 × T) / 100. Step 4: 3600 = 1200T, so T = 3 years.

Question 22

A person invests ₹6,000 at 15% simple interest per annum for 2 years and another ₹4,000 at 12% simple interest per annum for 3 years. What is the difference between the two interests earned?

Accepted Answer

Step 1: Calculate SI on first investment: SI₁ = (6,000 × 15 × 2) / 100 = 180,000 / 100 = ₹1,800. Step 2: Calculate SI on second investment: SI₂ = (4,000 × 12 × 3) / 100 = 144,000 / 100 = ₹1,440. Step 3: Difference = SI₁ - SI₂ = 1,800 - 1,440 = ₹360. Therefore, the difference is ₹360.

Question 23

Priya lent ₹12,000 to a friend at 10% simple interest per annum. After 2 years, her friend repaid ₹2,400 and promised to pay the remaining amount after another 1 year at the same rate. How much will Priya receive in total after 3 years from the date of lending?

Accepted Answer

Step 1: Calculate SI for first 2 years: SI = (12,000 × 10 × 2) / 100 = 2,400. Amount after 2 years = 12,000 + 2,400 = 14,400. Step 2: Friend repays ₹2,400, so remaining principal = 14,400 − 2,400 = 12,000. Step 3: For the next 1 year, SI on ₹12,000 = (12,000 × 10 × 1) / 100 = 1,200. Step 4: Final amount = 12,000 + 1,200 = 13,200. Step 5: Total received = 2,400 (after 2 years) + 13,200 (after 3 years) = 15,600.

Question 24

A sum of money doubles itself in 10 years at simple interest. At what rate per annum is the money invested?

Accepted Answer

Step 1: If principal is P, then final amount A = 2P (doubles). Step 2: SI = A - P = 2P - P = P. Step 3: Use SI = (P × R × T) / 100. Step 4: P = (P × R × 10) / 100. Step 5: Divide both sides by P: 1 = (R × 10) / 100. Step 6: R × 10 = 100. Step 7: R = 10% per annum. Therefore, the rate is 10% per annum.

Question 25

Rajesh borrowed ₹15,000 at 8% simple interest per annum. After how many years will the total amount (principal + interest) become ₹19,800?

Accepted Answer

Step 1: Use formula A = P + SI, where A = P(1 + RT/100). Step 2: 19,800 = 15,000(1 + 8T/100). Step 3: 19,800/15,000 = 1 + 8T/100. Step 4: 1.32 = 1 + 8T/100. Step 5: 0.32 = 8T/100. Step 6: T = (0.32 × 100) / 8 = 32/8 = 4 years. Therefore, the time period is 4 years.

Question 26

Two amounts are invested at 10% simple interest per annum. The first amount of ₹5,000 is invested for 4 years, and the second amount of ₹3,000 is invested for 6 years. What is the total interest earned from both investments?

Accepted Answer

Step 1: Calculate SI on first amount: SI₁ = (5,000 × 10 × 4) / 100 = 200,000 / 100 = ₹2,000. Step 2: Calculate SI on second amount: SI₂ = (3,000 × 10 × 6) / 100 = 180,000 / 100 = ₹1,800. Step 3: Total interest = SI₁ + SI₂ = 2,000 + 1,800 = ₹3,800. Therefore, total interest is ₹3,800.

Question 27

A sum of ₹8,000 is invested at a simple interest rate of 12% per annum. How much interest will be earned in 3 years and 6 months?

Accepted Answer

Step 1: Identify SI formula: SI = (P × R × T) / 100. Step 2: P = ₹8,000, R = 12% p.a., T = 3.5 years. Step 3: SI = (8000 × 12 × 3.5) / 100 = (336,000) / 100 = ₹3,360. Therefore, the interest earned is ₹3,360.

Question 28

A certain sum of money doubles itself in 10 years at simple interest. In how many years will it become 5 times itself at the same rate of interest?

Accepted Answer

Step 1: If principal = P, and it doubles in 10 years, then SI = P (since Amount = P + SI = 2P). Step 2: Using SI = (P × R × T) / 100, we have P = (P × R × 10) / 100. Step 3: Simplify: 1 = R × 10 / 100, so R = 10% per annum. Step 4: For amount to become 5 times, we need Amount = 5P, so SI = 4P. Step 5: Using SI = (P × R × T) / 100: 4P = (P × 10 × T) / 100. Step 6: Simplify: 4 = 10T / 100, so 4 = T / 10, thus T = 40 years.

Question 29

A sum of ₹8,000 is divided into two parts. The first part is lent at 12% simple interest and the second part at 10% simple interest, both for 3 years. If the total interest earned is ₹2,520, what is the first part?

Accepted Answer

Step 1: Let first part = P₁ and second part = P₂. We have P₁ + P₂ = 8,000. Step 2: SI from first part = (P₁ × 12 × 3)/100 = 0.36P₁. Step 3: SI from second part = (P₂ × 10 × 3)/100 = 0.3P₂. Step 4: Total SI = 0.36P₁ + 0.3P₂ = 2,520. Step 5: From P₁ + P₂ = 8,000, we get P₂ = 8,000 - P₁. Step 6: Substitute: 0.36P₁ + 0.3(8,000 - P₁) = 2,520 → 0.36P₁ + 2,400 - 0.3P₁ = 2,520 → 0.06P₁ = 120 → P₁ = 2,000.

Question 30

Two sums of money are in the ratio 3:5. They are lent at simple interest rates of 5% and 4% per annum respectively. After 4 years, the difference in the interests earned is ₹160. What is the larger sum?

Accepted Answer

Step 1: Let the two sums be 3x and 5x. Step 2: SI on first sum (3x at 5% for 4 years) = (3x × 5 × 4)/100 = 0.6x. Step 3: SI on second sum (5x at 4% for 4 years) = (5x × 4 × 4)/100 = 0.8x. Step 4: Difference in interests = 0.8x - 0.6x = 0.2x = 160. Step 5: x = 160 ÷ 0.2 = 800. Step 6: Larger sum = 5x = 5 × 800 = ₹4,000.

Question 31

A person invests ₹5,000 at 6% simple interest per annum. After how many years will the interest earned be equal to 60% of the principal?

Accepted Answer

Step 1: Principal = ₹5,000. Rate = 6% per annum. Step 2: Interest to be earned = 60% of Principal = 0.60 × 5,000 = ₹3,000. Step 3: Use SI formula: SI = (P × R × T)/100 → 3,000 = (5,000 × 6 × T)/100. Step 4: 3,000 = 300T. Step 5: T = 3,000 ÷ 300 = 10 years.

RRB NTPC Simple Interest

RRB NTPC Simple Interest — Past Exam Questions

Simple Interest— Rules & Concept

Key Points to Remember

Exam-Specific Tips

Simple Interest — Practice Questions

60-Second Revision — Simple Interest