Mathematics — Simple Interest

गणित — साधारण ब्याज

When money is borrowed or invested for a certain period, an additional amount paid or received for the use of that money is called interest.

जब किसी धनराशि को निश्चित समय के लिए उधार लिया या निवेश किया जाता है, तो मूल धन के अतिरिक्त दी या प्राप्त की जाने वाली राशि ब्याज कहलाती है।

Principal / मूलधन

The original amount borrowed or invested is called Principal (P).

मूल रूप से उधार ली गई या निवेश की गई राशि को मूलधन (P) कहते हैं।

Rate / ब्याज दर

The percentage of interest charged per year is called Rate (R).

प्रति वर्ष लगाए जाने वाले ब्याज प्रतिशत को दर (R) कहते हैं।

Time / समय

The period for which money is borrowed or invested is Time (T).

Simple Interest Formula

SI = (P × R × T)/100

Where:

P = Principal
R = Rate % per annum
T = Time in years

हिंदी में:

साधारण ब्याज = (मूलधन × दर × समय)/100

Amount / मिश्रधन

Amount = Principal + Interest

A = P + SI

Finding Principal

From:

SI = PRT/100

Therefore:

P = (SI × 100)/(R × T)

Finding Rate

R = (SI × 100)/(P × T)

Finding Time

T = (SI × 100)/(P × R)

Months to Years

If time is given in months:

T = Number of months/12

Example:

₹8,000 at 12% for 9 months.

T=9/12=3/4 year.

SI:

=8000×12×3/(100×4)

= ₹720

Days to Years

Normally:

T = Days/365

unless the examination question explicitly specifies another convention.

When Amount Becomes n Times

Suppose a sum becomes twice itself under SI.

A=2P

Therefore:

SI=P.

If rate=10%:

P×10×T/100=P

T=10 years.

Important Shortcut

If a sum doubles in T years at simple interest:

Rate = 100/T

If it becomes three times:

Interest=2P

Rate = 200/T

Simple Interest — 30 Questions

साधारण ब्याज — 30 प्रश्न

Q1

Find SI on ₹1,000 at 10% per annum for 2 years.

₹1,000 पर 10% वार्षिक दर से 2 वर्षों का साधारण ब्याज ज्ञात करें।

A. ₹100
B. ₹150
C. ₹200
D. ₹220

Answer / उत्तर: C

Explanation: SI=1000×10×2/100=₹200.

Q2

SI on ₹5,000 at 8% for 3 years:

A. ₹1,000
B. ₹1,200
C. ₹1,400
D. ₹1,500

Answer: B

Q3

SI on ₹8,000 at 5% for 4 years:

A. ₹1,400
B. ₹1,500
C. ₹1,600
D. ₹1,800

Answer: C

Q4

Principal ₹4,000, rate 10%, time 3 years. Amount?

A. ₹4,800
B. ₹5,000
C. ₹5,200
D. ₹5,400

Answer: C

Q5

SI is ₹900 at 10% for 3 years. Principal?

A. ₹2,000
B. ₹2,500
C. ₹3,000
D. ₹3,500

Answer: C

Q6

SI on ₹6,000 for 2 years is ₹960. Rate?

A. 6%
B. 8%
C. 10%
D. 12%

Answer: B

Q7

₹5,000 earns ₹1,500 at 10% SI. Time?

A. 2 years
B. 3 years
C. 4 years
D. 5 years

Answer: B

Q8

SI on ₹12,000 at 6% for 5 years:

A. ₹3,200
B. ₹3,400
C. ₹3,600
D. ₹4,000

Answer: C

Q9

Amount on ₹10,000 at 8% SI for 2 years:

A. ₹11,200
B. ₹11,400
C. ₹11,600
D. ₹11,800

Answer: C

Q10

SI on ₹8,000 at 12% for 6 months:

A. ₹400
B. ₹480
C. ₹560
D. ₹960

Answer: B

Q11

SI on ₹15,000 at 8% for 9 months:

A. ₹800
B. ₹850
C. ₹900
D. ₹1,000

Answer: C

Q12

At what rate will ₹4,000 earn ₹800 in 4 years?

A. 4%
B. 5%
C. 6%
D. 8%

Answer: B

Q13

A sum becomes ₹7,000 from ₹5,000 in 5 years at SI. Rate?

A. 6%
B. 8%
C. 10%
D. 12%

Answer: B

Q14

A sum doubles in 10 years at SI. Rate?

A. 5%
B. 8%
C. 10%
D. 12%

Answer: C

Q15

A sum doubles in 8 years at SI. Rate?

A. 10%
B. 12.5%
C. 15%
D. 16%

Answer: B

Q16

At 5% SI, in how many years will a sum double?

A. 10
B. 15
C. 20
D. 25

Answer: C

Q17

A sum becomes three times itself in 20 years at SI. Rate?

A. 5%
B. 8%
C. 10%
D. 12%

Answer: C

Q18

A sum earns ₹2,400 SI in 4 years at 12%. Principal?

A. ₹4,000
B. ₹5,000
C. ₹6,000
D. ₹8,000

Answer: B

Q19

SI on a sum for 5 years at 8% is ₹2,000. Amount?

A. ₹6,000
B. ₹7,000
C. ₹7,500
D. ₹8,000

Answer: B

Explanation: P=2000×100/(8×5)=₹5,000. Amount=₹7,000.

Q20

A sum earns ₹600 in 2 years and ₹1,500 in 5 years at SI. Interest per year is:

A. ₹250
B. ₹300
C. ₹350
D. ₹400

Answer: B

Q21

If rate increases from 8% to 10%, additional SI on ₹5,000 for 4 years is:

A. ₹300
B. ₹350
C. ₹400
D. ₹500

Answer: C

Q22

Difference between SI at 12% and 8% on ₹10,000 for 3 years:

A. ₹1,000
B. ₹1,200
C. ₹1,400
D. ₹1,600

Answer: B

Q23

A person invests ₹6,000 at 10% and ₹4,000 at 5% for one year. Total interest?

A. ₹700
B. ₹750
C. ₹800
D. ₹850

Answer: C

Q24

At 15% SI, interest for 8 months on ₹12,000 is:

A. ₹1,000
B. ₹1,200
C. ₹1,400
D. ₹1,800

Answer: B

Q25

A sum becomes ₹13,500 in 5 years at 7% SI. Principal?

A. ₹9,000
B. ₹10,000
C. ₹11,000
D. ₹12,000

Answer: B

Q26

A sum doubles in 12 years at SI. In how many years will it become three times itself at the same rate?

A. 18
B. 20
C. 24
D. 36

Answer: C

Q27

A sum becomes 1.5 times itself in 5 years at SI. Rate?

A. 5%
B. 8%
C. 10%
D. 12%

Answer: C

Q28

SI on ₹2,500 at 16% for 15 months:

A. ₹400
B. ₹450
C. ₹500
D. ₹550

Answer: C

Q29

A sum at 8% SI amounts to ₹7,800 in 5 years. Principal?

A. ₹5,000
B. ₹5,500
C. ₹6,000
D. ₹6,500

Answer: B

Explanation: A=P(1+8×5/100)=1.4P. P=7800/1.4=₹5,571.43, so none of the options is correct.

Corrected Question: If the amount is ₹7,700, Principal = ₹5,500 (B).

Q30

A sum of ₹8,000 is divided into two parts and invested at 10% and 15%. Total annual interest is ₹1,000. Amount invested at 15%?

A. ₹3,000
B. ₹4,000
C. ₹5,000
D. ₹6,000

Answer: B