Simple Interest: Notes और MCQ Practice

आसान भाषा में

Simple Interest (SI) वह ब्याज है जो हर साल सिर्फ Principal (मूलधन) पर ही कैलकुलेट होता है। इसमें Interest पर Interest नहीं लगता, यानी हर साल का SI हमेशा Same रहता है। SSC CGL Exam के लिए यह सबसे आसान और Direct Scoring टॉपिक है!

Important Formulas

• Simple Interest (SI) = (P × R × T) ÷ 100
• Total Amount (A) = P + SI
• Principal (P) = (SI × 100) ÷ (R × T)
• Rate (R) = (SI × 100) ÷ (P × T)
• Time (T) = (SI × 100) ÷ (P × R)

2 Quick Tricks

1. n-Times Trick: अगर कोई Sum 'T' years में 'n' गुना (times) हो जाता है, तो Rate (R) = [(n - 1) ÷ T] × 100%
2. R = T Concept: अगर Rate % और Time (years) बराबर हों (R = T), और SI = (x ÷ y) × P हो, तो R या T = √(x ÷ y) × 10

2 Common Mistakes

1. Time Unit Error: Time अगर Months में दिया हो तो 12 से Divide करें, और Days में हो तो 365 से Divide करके Years में कन्वर्ट करना न भूलें।
2. Amount vs Principal Confusion: Question में "Sum becomes X" का मतलब X Total Amount (A) है, Principal (P) नहीं! P निकालने के लिए A − SI करें।

1. Concept

Simple Interest (SI) is the extra amount earned or paid on a principal amount (P) for a given period of time (T) at a fixed rate of interest per annum (R). The interest is calculated only on the original principal, not on the accumulated interest.

2. Important formulas / rules / facts

• Simple Interest: SI = P × R × T ÷ 100
• Amount (A) after T years: A = P + SI
• Principal from amount: P = A ÷ (1 + R×T÷100)
• Rate of interest: R = SI × 100 ÷ (P × T)
• Time (in years): T = SI × 100 ÷ (P × R)
• Interest is linear with time – double the time, double the interest (if P and R stay same).
• For months, convert to years: T (years) = number of months ÷ 12.

3. Solved examples (exam style)

Example 1

Question: A sum of Rs. 4,500 is lent at 8% per annum. Find the simple interest earned in 3 years.

Solution:

1. Identify P = 4500, R = 8, T = 3.
2. Apply SI formula: SI = 4500 × 8 × 3 ÷ 100.
3. Compute: 4500 × 8 = 36,000; 36,000 × 3 = 108,000; 108,000 ÷ 100 = Rs. 1,080.

Answer: Rs. 1,080.

Example 2

Question: The amount after 5 years is Rs. 7,500. If the rate of interest is 10% per annum, what was the principal?

Solution:

1. Let P be the principal. Amount A = P + SI.
2. SI = P × 10 × 5 ÷ 100 = P × 0.5.
3. Hence, A = P + 0.5P = 1.5P.
4. Given A = 7500, so 1.5P = 7500 → P = 7500 ÷ 1.5 = Rs. 5,000.

Answer: Rs. 5,000.

Example 3

Question: A man borrows Rs. 2,200 at a simple interest rate of 12% per annum. He repays the loan after 9 months. How much does he pay back?

Solution:

1. Convert time to years: T = 9 ÷ 12 = 0.75 years.
2. SI = 2200 × 12 × 0.75 ÷ 100.
3. 2200 × 12 = 26,400; 26,400 × 0.75 = 19,800; 19,800 ÷ 100 = Rs. 198.
4. Amount = Principal + SI = 2200 + 198 = Rs. 2,398.

Answer: Rs. 2,398.

Example 4

Question: Find the rate of interest per annum if Rs. 3,600 earns Rs. 540 as simple interest in 2 years.

Solution:

1. Use R = SI × 100 ÷ (P × T).
2. R = 540 × 100 ÷ (3600 × 2) = 54,000 ÷ 7,200 = 7.5%.

Answer: 7.5% per annum.

4. Shortcuts and tricks

• Quick amount formula: Amount = P × (1 + R×T÷100). Memorise the factor (1 + R×T÷100) for fast calculations.
• Pro‑rata method: When time is in months, directly use SI = P × R × (months) ÷ (12×100).
• Cross‑multiplication: For questions asking for one unknown (P, R, T, or SI), rearrange the basic SI formula by cross‑multiplying; this avoids fractions.
• Use of 5% rule: 5% of any number is half of 10% (i.e., divide by 20). Helpful when rate is 5% or multiples thereof.

5. Common mistakes to avoid

1. Mixing up time units: Always convert months to years (or days to years) before using the formula.
2. Adding interest twice: Remember that Amount = Principal + Simple Interest, not Principal × (1 + R×T÷100) × (1 + R×T÷100).
3. Wrong placement of 100: The divisor 100 belongs only to the product P×R×T, not to each term separately.
4. Using compound‑interest logic: Simple interest does not compound; do not apply (1 + R/100)^T.
5. Sign errors: Interest earned is positive; if a problem involves a loss, treat it as a negative interest but keep the formula unchanged.