Q: X lent ₹6,000 to Y for 3 years and ₹4,000 to Z for 2 years, both at the same simple interest rate. In total, he received ₹2,000 as interest from both. What is the rate of interest per annum (nearest integer)?

8%. Total simple interest = $\frac{6000\times 3\times r}{100} + \frac{4000\times 2\times r}{100}$ = $\frac{26000r}{100}$. This equals 2000, so r = 2000×100/26000 ≈ 7.69, which rounds to 8%.

Question 1

X lent ₹6,000 to Y for 3 years and ₹4,000 to Z for 2 years, both at the same simple interest rate. In total, he received ₹2,000 as interest from both. What is the rate of interest per annum (nearest integer)?

Accepted Answer

8%. Total simple interest = $\frac{6000\times 3\times r}{100} + \frac{4000\times 2\times r}{100}$ = $\frac{26000r}{100}$. This equals 2000, so r = 2000×100/26000 ≈ 7.69, which rounds to 8%.

Question 2

A person invests ₹24,000 in two schemes — Scheme A at 18% and Scheme B at 12%, both at simple interest. After 1 year, the total interest is ₹3,840. How much was invested in Scheme A?

Accepted Answer

₹ 16,000. If x is invested at 18%, then 24,000 − x is invested at 12%. The total interest equation is 0.18x + 0.12(24,000 − x) = 3,840. Solving gives x = ₹16,000.

Question 3

A certain amount grows to ₹8,000 in 2 years and to ₹8,800 in 3 years. Determine the simple interest rate per annum.

Accepted Answer

12.5%. Under simple interest, the yearly increase is constant. The amount rises from ₹8,000 to ₹8,800 in one year, so yearly interest is ₹800. Since ₹8,000 after 2 years means principal + 2 years’ interest = 8,000, the principal is ₹6,400, and the rate is 800/6400 × 100 = 12.5%.

Question 4

Karan borrowed money at simple interest: 6% for the first 4 years, 8% for the next 3 years, and 10% beyond 7 years. If the total interest after 9 years is ₹4,760, how much did he borrow?

Accepted Answer

₹ 7,000. For principal P, interest for 4 years at 6% = 0.24P, for next 3 years at 8% = 0.24P, and for last 2 years at 10% = 0.20P. Total interest = 0.68P. Given total interest ₹4760, P = 4760/0.68 = ₹7000.

Question 5

A sum becomes 2.5 times in 10 years under simple interest. Find the rate.

Accepted Answer

15%. If the sum becomes 2.5 times, the amount is 2.5P, so the simple interest is 1.5P. Using SI = PRT/100, we get 1.5P = P × R × 10 / 100, which gives R = 15%.

Question 6

Kavya invested amounts in three schemes P, Q, and R at simple interest rates of 11% p.a., 13% p.a., and 16% p.a. respectively. If the total interest in one year was ₹2,850 and the amount in Scheme R was 200% of Scheme P and 300% of Scheme Q, what was the amount invested in Scheme Q?

Accepted Answer

₹ 3677. Let the investment in P be x, in Q be y, and in R be 2x. Also, R is 300% of Q, so 2x = 3y, hence x = 1.5y. Total interest for one year is 11% of x + 13% of y + 16% of 2x = 2850. Solving gives y = 3676.92, which rounds to ₹3677.

Question 7

Priya borrowed ₹40,000 from two lenders under simple-interest terms: Lender M charges 8% p.a. and Lender N charges 5% p.a. Priya kept both loans for exactly 5 years and then paid the accumulated interest, which was ₹14,000. If she had interchanged the principal amounts, her five-year inter

Accepted Answer

₹ 26,667. Let the amount borrowed from M be x and from N be 40000 - x. The 5-year interest is 0.4x + 0.25(40000 - x) = 14000, which gives x = 26666.67. This matches ₹26,667, and swapping the principals reduces the interest by ₹2000 as stated.

Question 8

₹800 is lent at a certain rate of simple interest. After 4 months, another ₹1200 is lent at a rate which is twice the original rate. If the total simple interest after 1 year is ₹96, find the original rate.

Accepted Answer

4%. The first ₹800 earns interest for 1 year at rate $r\%$. The second ₹1200 is lent after 4 months, so it earns interest for 8 months at rate $2r\%$. Adding both interests and equating to ₹96 gives $800\cdot r\cdot 1/100 + 1200\cdot 2r\cdot (8/12)/100 = 96$, which yields $r=4\%$.

Question 9

A sum of ₹12000 is divided into two parts and lent at 6% and 11% simple interest respectively. If the total annual interest earned is ₹960, find the amount lent at 11%.

Accepted Answer

₹ 4800. If $x$ is lent at 11%, then $12000-x$ is lent at 6%. The total interest in one year is $0.11x + 0.06(12000-x) = 960$. Solving gives $x=4800$.

Question 10

An amount of ₹8000 is divided into two parts. The first part is lent at 5% simple interest and the second at 8% simple interest. If the total annual interest earned is ₹520, find the sum lent at 5%.

Accepted Answer

₹ 4000. Let the sum lent at 5% be $x$. Then the remaining $8000-x$ is lent at 8%, and the total interest for one year is $0.05x+0.08(8000-x)=520$. Solving gives $x=4000$.

Question 11

A woman invests ₹20,000. She lends one part to A for 2 years at 8% per annum simple interest and the rest to B for 2 years at 12% per annum simple interest. If the total interest from both is ₹4,160, find the amount lent to A.

Accepted Answer

₹ 8,000. Let the amount lent to A be $x$. Then interest from A is $x	imes 8	imes 2/100=0.16x$, and from B is $(20000-x)	imes 12	imes 2/100=0.24(20000-x)$. Adding and equating to ₹4,160 gives $0.16x+0.24(20000-x)=4160$, which solves to $x=8000$.

Question 12

X borrowed ₹8000 from Y on 10 January 2024 at a simple interest rate of 12% per annum. X decided to repay the loan on 10 July 2024. How much total amount must X return to Y?

Accepted Answer

₹ 8480. The time is 6 months = $	frac{1}{2}$ year. Simple interest $= \frac{8000 	imes 12 	imes 1/2}{100} = 480$. So the total amount is $8000 + 480 = 8480$.

Question 13

A person invested a total sum of ₹4500 in three different schemes of simple interest at 3%, 4%, and 6% per annum. At the end of one year, he got the same interest from all three schemes. What was the amount (in ₹) invested at 4%?

Accepted Answer

₹ 1500. Since the interest for 1 year is the same in all three schemes, the invested amounts are inversely proportional to the rates. Thus the ratio of investments is $\frac{1}{3}:\frac{1}{4}:\frac{1}{6} = 4:3:2$. The total 9 parts correspond to ₹4500, so 1 part = ₹500 and the amount at 4% is 3 parts = ₹1500.

Question 14

Amit borrowed Rs. 1500 at simple interest for a number of years equal to the rate of interest. At the end of the loan term, he paid Rs. 540 as interest. What was the rate of interest?

Accepted Answer

6%. Let the rate be $r\%$, so time is also $r$ years. Using $SI = \frac{PRT}{100}$, we get $540 = \frac{1500\cdot r\cdot r}{100}$, which gives $r^2=36$ and hence $r=6$.

Question 15

A person invested ₹15,000 in two different schemes. He invested one part for 5 years at 4% simple interest and the other part for the same duration at 6% simple interest. If the interest earned from the second part was ₹1,500 more than the interest earned from the first part, how much mone

Accepted Answer

₹ 9,000. Let the amount invested at 6% be $x$, so the amount at 4% is $15000-x$. The difference in interest for 5 years is $\frac{x\cdot 6\cdot 5}{100}-\frac{(15000-x)\cdot 4\cdot 5}{100}=1500$. Solving gives $x=9000$.

Question 16

A person invested ₹12,000 at 5% simple interest and ₹8,000 at 10% simple interest for the same period. If the total interest earned is ₹2,800, what was the time duration?

Accepted Answer

2 years. Interest from ₹12,000 at 5% for $t$ years is $12000	imes5	imes t/100=600t$. Interest from ₹8,000 at 10% is $8000	imes10	imes t/100=800t$. Total interest is $1400t=2800$, so $t=2$ years.

Question 17

At what rate of simple interest per annum will ₹5,000 amount to ₹6,500 in 3 years?

Accepted Answer

10%. The simple interest is $6500-5000=1500$. Using $SI=\frac{PRT}{100}$, we get $1500=\frac{5000\times R\times 3}{100}$, so $R=10\%$.

Question 18

A sum of money triples itself in 8 years at simple interest. In how many years will it become 7 times itself at the same rate of interest?

Accepted Answer

24 years. At simple interest, tripling means the interest earned in 8 years equals 2 times the principal. So the yearly interest is $\frac{2P}{8}=\frac{P}{4}$. To become 7 times, the interest must be 6 times the principal, which takes $6P \div \frac{P}{4}=24$ years.

Question 19

A person invested a total sum of ₹2700 in three different schemes of simple interest at 3%, 4%, and 6% per annum. At the end of one year, he got the same interest from all three schemes. What was the amount (in ₹) invested at 4%?

Accepted Answer

₹ 900. If the interest earned in one year is the same, then principal amounts are inversely proportional to the rates. So the investments are in the ratio $\frac{1}{3}:\frac{1}{4}:\frac{1}{6}=4:3:2$. Their sum is 9 parts, equal to ₹2700, so 1 part = ₹300. Hence the amount at 4% is 3 parts = ₹900.

Question 20

A sum becomes 3 times itself in 8 years under simple interest. In how many years will it become 7 times itself at the same rate?

Accepted Answer

24 years. If a sum becomes 3 times in 8 years, then simple interest in 8 years is 2 times the principal. So the rate of increase is $2/8=1/4$ principal per year. To become 7 times, the interest must be 6 times the principal, which takes $6\div(1/4)=24$ years.

Question 21

A businessman took a loan of ₹12,000 from a bank on 1 May 2025 at simple interest of 8% per annum. He decided to clear the loan on 1 November 2025. How much amount did he pay back to the bank?

Accepted Answer

₹12,480. Time = 6 months = $\frac{1}{2}$ year. Simple interest = $\frac{P\times R\times T}{100} = \frac{12000\times 8\times 1/2}{100} = 480$. Total amount = $12000+480=12480$.

Question 22

A certain sum becomes 5 times itself in 12 years at simple interest. In how many years will it become 9 times itself at the same rate?

Accepted Answer

24 years. If the sum becomes 5 times in 12 years, the simple interest earned in 12 years is 4 times the principal. So yearly interest is one-third of the principal. To become 9 times, the interest must be 8 times the principal, which takes 24 years.

Question 23

If the simple interest on a sum of Rs. P at 8% per annum for 3 years is equal to the simple interest on Rs. Q at 6% per annum for 4 years, then what is the ratio of P to Q?

Accepted Answer

1:1. Simple interest is proportional to principal × rate × time. So $P	imes 8	imes 3 = Q	imes 6	imes 4$, which simplifies to $24P=24Q$. Hence, $P:Q=1:1$.

Question 24

A sum amounts to ₹6,600 in 2 years and ₹7,200 in 4 years at simple interest. What is the rate of interest per annum?

Accepted Answer

5%. The amount increases from ₹6,600 to ₹7,200 in 2 years, so the simple interest for 2 years is ₹600. Therefore, yearly interest is ₹300, and the principal is ₹6,600 - ₹600 = ₹6,000. Rate = (300/6000) × 100 = 5%.

Question 25

What is the ratio of the simple interest earned on a given amount at the same rate of interest over 6 years to that earned over 9 years?

Accepted Answer

2:3. In simple interest, for the same principal and rate, interest is proportional to time. So the ratio of interest for 6 years and 9 years is 6:9, which simplifies to 2:3.

Question 26

A donor deposits ₹8,00,000 in a trust that earns 10% simple interest annually. The interest is used to distribute three annual awards. If the second and third awards are ₹35,000 and ₹20,000 respectively, what is the value of the first award?

Accepted Answer

25,000. The annual simple interest is 10% of ₹8,00,000 = ₹80,000. If the second and third awards are ₹35,000 and ₹20,000, the first award is ₹80,000 - ₹35,000 - ₹20,000 = ₹25,000.

Question 27

If $P = 	ext{Rs. }1500$, $R = 8.5\%$, and $T = 2.5$ years, find the simple interest.

Accepted Answer

Rs. 318.75. Simple interest is given by $SI = \frac{P	imes R	imes T}{100}$. Substituting the values gives $\frac{1500	imes 8.5	imes 2.5}{100} = 318.75$. Hence, the simple interest is Rs. 318.75.

Question 28

In how many years will a sum of Rs. 4,000 give a simple interest of Rs. 1,200 at 10% per annum?

Accepted Answer

3 years. Using the simple interest formula, $SI = \frac{PRT}{100}$. Substituting the values gives $1200 = \frac{4000 \times 10 \times T}{100}$, so $T = 3$ years.

Question 29

Consider the following statements regarding simple interest: 1. The simple interest on Rs. 8,000 for 3 years at 5% per annum is Rs. 1,200. 2. If a sum of money doubles in 10 years at simple interest, then it will become 1.5 times in 6 years. 3. The simple interest rate required for an amou

Accepted Answer

1 and 3 are correct. Statement 1 is correct because SI = $8000 \times 5 \times 3 /100 = 1200$. Statement 2 is false because if money doubles in 10 years, then SI in 10 years equals principal, so in 6 years it becomes 1.6 times, not 1.5 times. Statement 3 is correct because to become 2.5 times in 5 years, SI = 1.5P, so rate = $1.5 \times 100 / 5 = 30\%$.

SSC CGL (Prelims) General: Simple Interest questions with solutions

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