Detailed Solutions: Simple Interest
Simple Interest (SI) is one of the most important topics in Mathematics for SSC, Banking, Railway, NDA, and other competitive exams. Questions from simple interest are frequently asked in arithmetic and word-problem sections.
Here, you will find the Top 4 Important Simple Interest Questions with Answers to help you prepare effectively.
What is Simple Interest in Mathematics?
Simple Interest is the interest calculated on the original principal amount for a fixed period of time.
Simple interest = \( \frac{ P × R × T }{100}\)
Where
P = Principal
R = Rate of interest
T = Time (in years)
Question: 1
₹4,000 को दो भागों में इस प्रकार बाँटा गया कि पहले भाग पर 3% और दूसरे पर 5% ब्याज मिलता है। यदि पूरे वर्ष का कुल ब्याज ₹144 है, तो प्रत्येक भाग ज्ञात करें।
₹4,000 is divided into two parts such that the first part earns 3% interest and the second 5% interest. If the total interest for the entire year is ₹144, find the interest on each part.
[A] 2800, 1200 [B] 2000, 1200
[C] 2800, 5600 [D] 2800, 2000
⚡Solution:
Answer (a) : माना पहला भाग A है तथा इसरा भाग ( 4000- A )
पहले भाग पर 3% ब्याज = \(\frac{A × 3 × 1}{100} = \frac{3A}{100}\)
दूसरे भाग पर 5% ब्याज = \(\frac{(4000-A) × 5 × 1}{100}\)
\(\frac{4000 × 5 × 1}{100} – \frac{A × 5 × 1}{100} \)
\(200 – \frac{5A}{100}\)
दोनों भागों से प्राप्त कुल ब्याज = 144
\(\frac{3A}{100} + 200 – \frac{5A}{100} = 144\)
\(200 – 144 = \frac{5A}{100} – \frac{3A}{100}\)
\(56 = \frac{5A}{100} – \frac{3A}{100}\)
\(5600 = 5A – 3A\)
\( A = 2800 \)
पहला भाग = ₹2800
दूसरा भाग = ₹4000 – ₹2800 = ₹1200
Question: 2
कोई धन साधारण ब्याज की दर से 3 वर्ष में ₹575 और 5 वर्ष में ₹625 हो जाता है। ब्याज की दर ज्ञात करें।
A sum of money amounts to ₹575 in 3 years and ₹625 in 5 years at simple interest. Find the rate of interest.
[A] 50% [B] 5%
[C] 25% [D] 10%
⚡Solution:
Answer (b) : 5%
Step-1: 2 वर्ष का ब्याज = 625 – 575 = 50.
1 वर्ष का ब्याज = ₹25.
3 वर्ष का ब्याज = 25 × 3 = 75.
Step-2: मूलधन (P) = 575 – 75 = 500
Step-3: formula; Rate = \( \frac{ Interest × 100}{ Principal amount × time}\)
R = \(\frac{25 × 100}{500 × 1}\)
R = 5
ब्याज की दर : 5%
Question: 3
किसी राशि पर साधारण ब्याज, मूलधन का \(1/9\) है। यदि वर्षों की संख्या और वार्षिक दर प्रतिशत संख्यात्मक रूप से समान हों, तो दर ज्ञात करें।
The simple interest on a sum is \(1/9 \)of the principal. If the number of years and the annual rate percent are numerically equal, find the rate.
[A] 5% [B] 10%
[C] 9% [D] 3.33%
⚡Solution:
Answer (d) : 3.33%
Step-1: दिया है : साधारण ब्याज, मूलधन का 1/9
अर्थात् जब मूलधन 9 इकाई होगा तब साधारण ब्याज 1 होगा ।
माना मूलधन P = 9 तथा ब्याज = 1
Note : वर्षों की संख्या और वार्षिक दर प्रतिशत संख्यात्मक रूप से समान हैं अर्थात् R = T
Step-2: formula; Simple interest = \( \frac{ P × R × T }{100}\)
\( 1 = \frac{ 9 × R × R }{100}\)
\( 100 = 9 × R^2 \)
\( R^2 = \frac{ 100}{9}\)
वर्ग हटाने के लिए वर्गमूल करें।
\( R= \frac{ 10}{3} = 3.33 \)
ब्याज की दर R = 3.33%
Why Simple Interest Questions Are Important for Exams
- Frequently asked in SSC, Banking, Railway, and State exams
- Easy and high-scoring topic
- Used in real-life financial calculations
- Helps in understanding compound interest
Conclusion
Practicing these Simple Interest important questions will improve your accuracy and confidence in exams. This chapter is one of the most scoring parts of arithmetic.