Question 1

A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest?

Accepted Answer

Given Principal P = Rs. 12,500 Amount A = Rs. 15,500 Time t = 4 years Simple InterestSI = A − P = 15,500 − 12,500 = 3,000SI = 𝑃 × 𝑟 × 𝑡 100 100 P×r×t ⇒ 3,000 = 12 , 500 × 𝑟 × 4 100 100 12,500×r×4 3,000 = 500r ⇒ r = 3 , 000 500 500 3,000 = 6% per annum

Question 2

Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?

Accepted Answer

Given Principal P = Rs. 1200 Simple interest SI = Rs. 432 Time (years) equals rate r (in %), i.e., t = r ComputeSI = 𝑃 × 𝑟 × 𝑡 100 100 P×r×t = 1200 × 𝑟 × 𝑟 100 100 1200×r×r = 12r^212r^2 = 432 ⇒ r^2 = 36 ⇒ r = 6%

Question 3

How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?

Accepted Answer

Given Principal P = Rs. 450 Simple interest SI = Rs. 81 Rate r = 4.5% p.a. Time via simple interestSI = 𝑃 × 𝑟 × 𝑡 100 100 P×r×t ⇒ 81 = 450 × 4.5 × 𝑡 100 100 450×4.5×t 81 = 20.25t ⇒ t = 81 20.25 20.25 81 = 4 years

Question 4

A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum?

Accepted Answer

Given Total Simple Interest (SI) = Rs. 4016.25 Rate (r) = 9% per annum Time (t) = 5 years FormulaSI = (P × r × t) / 100⇒ P = (SI × 100) / (r × t) Substitute valuesP = (4016.25 × 100) / (9 × 5)= 401625 / 45= 8925 Final AnswerThe principal (sum) is Rs. 8,925.

Question 5

A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:

Accepted Answer

Given Amount after 3 years = Rs. 815 Amount after 4 years = Rs. 854 Idea: In simple interest the interest per year is constant. The increase from year 3 to year 4 equals the interest of one year. 1 year's interest = 854 − 815 = 39Interest in 3 years = 3 × 39 = 117Principal P = Amount after 3 years − interest for 3 yearsP = 815 − 117 = Rs. 698 CheckInterest in 4 years = 4 × 39 = 156; P = 854 − 156 = 698 ✓

Question 6

A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is:

Accepted Answer

Given Amount after 5 years = Rs. 9,800 Amount after 8 years = Rs. 12,005 Step 1: Find annual interestIncrease over 3 years = 12,005 − 9,800 = 2,205So, interest per year I = 2,205 / 3 = 735 Step 2: Find principalAfter 5 years: A = P + 5I ⇒ 9,800 = P + 5 × 735P = 9,800 − 3,675 = 6,125 Step 3: Rater = (I / P) × 100 = (735 / 6,125) × 100 = 12% per annum

Question 7

Mr. Thomas invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount investe…

Accepted Answer

Given Total investment = Rs. 13,900 split into Scheme A (14% p.a.) and Scheme B (11% p.a.). Total simple interest in 2 years = Rs. 3,508. Let amount in A = x, amount in B = y. Then x + y = 13,900. Interest for 2 years0.14 × 2 × x + 0.11 × 2 × y = 3,5080.28x + 0.22y = 3,508Using y = 13,900 − x:0.28x + 0.22(13,900 − x) = 3,5080.28x + 3,058 − 0.22x = 3,508 ⇒ 0.06x = 450 ⇒ x = 7,500Hence y = 13,900 − 7,500 = Rs. 6,400

Question 8

A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is:

Accepted Answer

Given Rs. 5,000 lent for 2 years Rs. 3,000 lent for 4 years Total simple interest received = Rs. 2,200 at the same rate r. ComputeTotal SI = (5000 × r × 2)/100 + (3000 × r × 4)/100= r/100 × (10,000 + 12,000) = 220r220r = 2,200 ⇒ r = 10% per annum

Question 9

An automobile financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes:

Accepted Answer

Concept: The financier says simple interest but adds interest to principal every six months → effectively compound interest (half-yearly). Given: Nominal rate = 10% p.a. ⇒ 5% per half-year. Effective annual rate(1 + 0.05)^2 − 1 = 1.1025 − 1 = 0.1025 = 10.25% Thus, the effective rate of interest is 10.25%.

Question 10

A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was:

Accepted Answer

Given data Simple Interest (SI) paid after 3 years = Rs. 5400 Rate of interest r = 12% p.a. Time t = 3 years Formula SI = (P × r × t) ÷ 100 Step 1: Substitute values5400 = (P × 12 × 3) ÷ 1005400 = (36P) ÷ 100 Step 2: Solve for principal PP = 5400 × 100 ÷ 36P = 540000 ÷ 36 = Rs. 15,000 Final Answer: The principal amount borrowed was Rs. 15,000.

Question 11

A sum of Rs. 725 is lent in the beginning of a year at a certain rate of interest. After 8 months, a sum of Rs. 362.50 more is lent but at the rate twice the former. At the end of the year, Rs. 33.50 is earned as interest from both the loans. What w…

Accepted Answer

Given data Loan 1: Rs. 725 for the whole year at r% p.a. Loan 2: After 8 months, lend Rs. 362.50 for the remaining 4 months at twice the former rate = 2r% p.a. Total interest earned in the year = Rs. 33.50 Step 1: Interest from the first loanI1 = 725 × r × 1 ÷ 100 = 7.25r Step 2: Interest from the second loanTime for second loan = 4 months = 4/12 yearsI2 = 362.50 × (2r) × (4/12) ÷ 100= 362.50 × 2r × 1/3 ÷ 100= (725/3) × r ÷ 100 = (7.25/3)r Step 3: Total interest equationI1 + I2 = 7.25r + (7.25/3)r = (29/3)r(29/3)r = 33.50r = 33.50 × (3/29) = 3.465517241... % p.a.≈ 3.47% p.a. Final Answer: Original rate of interest = 3.47% per annum.

Question 12

A certain amount earns simple interest of Rs. 1750 after 7 years. Had the interest been 2% more, how much more interest would it have earned?

Accepted Answer

Given Simple interest for 7 years = Rs. 1750 Hence, simple interest per year = 1750 ÷ 7 = Rs. 250 Rate increased by 2 percentage points (i.e., +2% p.a.) Concept Under Simple Interest, extra interest due to a change in rate is proportional to the principal and time: ΔSI = P × (Δr) × t ÷ 100. Step 1: Recover principal from yearly SIYearly SI = (P × r) ÷ 100 = 250A convenient integer pair that fits the data is r = 10% ⇒ P = 250 × 100 ÷ 10 = 2500(Any admissible pair (P, r) that satisfies the yearly SI gives the same extra SI below because we use P directly.) Step 2: Extra SI for +2% over 7 yearsΔSI = P × 2 × 7 ÷ 100 = 2500 × 14 ÷ 100 = Rs. 350 Final Answer: Additional interest earned would be Rs. 350.

Question 13

A person borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6¼% p.a for 2 years. Find his gain in the transaction per year.

Accepted Answer

Given Borrows Rs. 5000 @ 4% p.a. for 2 yrs ⇒ Pays SIout Lends same Rs. 5000 @ 6¼% p.a. for 2 yrs ⇒ Receives SIin Step 1: Compute both interestsSIout = 5000 × 4 × 2 ÷ 100 = Rs. 400SIin = 5000 × 6.25 × 2 ÷ 100 = Rs. 625 Step 2: Net gainNet (2 years) = 625 − 400 = Rs. 225Per year gain = 225 ÷ 2 = Rs. 112.50 Final Answer: Net gain per year = Rs. 112.50.

Question 14

What will be the ratio of simple interest earned by certain amount at the same rate of interest for 6 years and that for 9 years?

Accepted Answer

Concept For a fixed principal and rate, Simple Interest is directly proportional to time (SI ∝ t). StepRequired ratio = SI for 6 years : SI for 9 years = 6 : 9 = 2 : 3 Final Answer: 2 : 3.

Question 15

What principal is required to earn a monthly interest of Rs 400 at 10% per annum (simple interest)?

Accepted Answer

Introduction / Context:Simple interest (SI) per period equals Principal * Rate per period. Convert annual rate to a monthly rate to find the principal that yields a target monthly interest. Given Data / Assumptions: Monthly interest desired = Rs 400. Annual rate = 10% → monthly rate = 10% / 12 = 0.10/12. Concept / Approach:SI_month = P * r_month → P = SI_month / r_month. Step-by-Step Solution:P = 400 / (0.10/12) = 400 * 12 / 0.10 = 48,000. Verification / Alternative check:Monthly SI on 48,000 at 10% p.a. = 48,000 * 0.10 / 12 = 400. Why Other Options Are Wrong:2,000/12,000/24,000 produce insufficient monthly interest at the given rate. Common Pitfalls:Using 10% as monthly instead of annual; forgetting to divide by 12. Final Answer:Rs 48,000

Question 16

For what time t (in years) will the simple interest on Rs 400 at 10% per annum equal the simple interest on Rs 1000 for 4 years at 4% per annum?

Accepted Answer

Introduction / Context:Equate two simple-interest amounts. For SI, I = P * R * T (with R in per-year fraction). Solve for the unknown time t. Given Data / Assumptions: I1 (on Rs 400 at 10% for t years) = 400 * 0.10 * t. I2 (on Rs 1000 at 4% for 4 years) = 1000 * 0.04 * 4. Concept / Approach:Set I1 = I2 and solve for t. Step-by-Step Solution:400 * 0.10 * t = 1000 * 0.04 * 4 → 40 t = 160 → t = 4 years. Verification / Alternative check:I1 = 40*4 = 160; I2 = 1000*0.16 = 160; equal. Why Other Options Are Wrong:2, 3, 6 years give mismatched interest amounts. Common Pitfalls:Mixing percentage and decimal forms; forgetting to multiply 4% by 4 years. Final Answer:4 yrs

Question 17

At what annual simple-interest rate will a sum of money double in 8 years?

Accepted Answer

Introduction / Context:Under simple interest, amount A = P * (1 + r * t). Doubling means A = 2P, so 1 + r * t = 2 → r * t = 1. Given Data / Assumptions: t = 8 years. Simple interest model. Concept / Approach:r = 1 / t (in decimal). Step-by-Step Solution:r = 1 / 8 = 0.125 = 12.5% per annum. Verification / Alternative check:Check: A = P (1 + 0.125 * 8) = P * 2 = 2P. Why Other Options Are Wrong:12% gives 1.96P; 13% gives 2.04P; 15% gives 2.20P in 8 years. Common Pitfalls:Applying compound-interest logic; here the model is simple interest. Final Answer:12.5 %

Question 18

Simple Interest – Find principal and rate from two amounts at different times: A certain principal amounts to Rs 1,586 in 2 years and Rs 1,729 in 3 years at simple interest. Determine (i) the annual rate of interest and (ii) the original principal (…

Accepted Answer

Introduction / Context:In simple interest (SI), the interest earned per year is constant. When two amounts are given at two successive times, the yearly interest can be obtained from the difference of the amounts. This allows us to back-calculate both the principal and the rate. Given Data / Assumptions: Amount in 2 years, A2 = Rs 1586 Amount in 3 years, A3 = Rs 1729 Simple interest model: A = P * (1 + r * t), with r in decimal per year Concept / Approach:The increase from year 2 to year 3 equals one year of simple interest. Thus annual SI = A3 - A2. Then P = A2 - 2 * (annual SI). The rate r = (annual SI / P) * 100 percent per annum. Step-by-Step Solution: Annual SI = 1729 - 1586 = Rs 143Principal P = 1586 - 2 * 143 = 1586 - 286 = Rs 1300Rate r% = (Annual SI / P) * 100 = (143 / 1300) * 100 = 11% Verification / Alternative check: Amount in 3 years by formula = 1300 * (1 + 0.11 * 3) = 1300 * 1.33 = Rs 1729 (matches) Why Other Options Are Wrong: 9% and Rs 1300: rate too low for the observed yearly increase. 10% and Rs 1200: would give annual SI of Rs 120, not Rs 143. 11% and Rs 1200: inconsistent with A2. 10% and Rs 1300: annual SI would be Rs 130, not Rs 143. Common Pitfalls: Using compound interest logic instead of simple interest. Subtracting total times instead of recognizing annual increment equals the difference of consecutive amounts. Final Answer:Rate = 11% per annum and Principal = Rs 1300.

Question 19

Simple Interest – Find original principal from amount: At 5% per annum simple interest, a sum of money amounts to Rs 900 in 4 years. Find the original principal (sum).

Accepted Answer

Introduction / Context:Given the final amount under simple interest, we can recover the principal using the linear growth model A = P * (1 + r * t). Given Data / Assumptions: A = Rs 900 r = 5% per annum t = 4 years Concept / Approach:Under SI, A = P * (1 + r * t). Rearranging, P = A / (1 + r * t). Use r = 0.05, t = 4. Step-by-Step Solution: 1 + r * t = 1 + 0.05 * 4 = 1.20P = 900 / 1.20 = Rs 750 Verification / Alternative check: Check: SI = P * r * t = 750 * 0.05 * 4 = 150; A = 750 + 150 = 900 (consistent) Why Other Options Are Wrong: Rs 650 / Rs 550 / Rs 500 / Rs 800: do not satisfy A = 900 under 5% for 4 years. Common Pitfalls: Mistaking compound interest for simple interest. Forgetting to convert percent to decimal. Final Answer:Rs 750.

Question 20

Simple Interest – Time to quadruple when doubling time is known: If a certain sum doubles itself in 8 years at simple interest, in how many years will it become four times the principal?

Accepted Answer

Introduction / Context:In simple interest, growth is linear with time. If we know the time to double, we can scale proportionally to find the time to quadruple the principal. Given Data / Assumptions: Doubling time t2 = 8 years Simple interest model Concept / Approach:Doubling at SI means interest equals P over 8 years, so r = 1 / 8 = 12.5% per annum. For quadrupling (A = 4P), interest must be 3P, so time t4 = 3P / (P * r) = 3 / r. Step-by-Step Solution: From doubling: r = 1 / 8 = 0.125 = 12.5%For A = 4P: required interest = 3Pt = 3P / (P * 0.125) = 3 / 0.125 = 24 years Verification / Alternative check: Linear scaling: Doubling needs 8 years; quadrupling needs twice the gain (from +P to +3P is 3 times P vs 1P), but relative to zero it is threefold interest. Time = 3 * 8 / 1? Using r is clearer; result 24 years. Why Other Options Are Wrong: 16/12/20 years: inconsistent with r = 12.5%. 32 years: overestimates required time. Common Pitfalls: Treating the process as compounding. Confusing quadruple of P with four times the interest. Final Answer:24 years.

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