What sum of money (in rupees) will yield 900 rupees as simple ... | Mathematics MCQ | Examoogle

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MathematicsSimple & Compound Interest

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What sum of money (in rupees) will yield 900 rupees as simple interest in 4 years at 5% per annum?

4000

4500

5000

5500

Correct Answer

📐 MA • Math Direct FormulaMathematicsSimple & Compound Interest

Option B

4500

Quick Summary:

Calculate the total percentage interest ( $R \times T = 5 \times 4 = 20\%$ ) and equate it to the interest amount ( $20\% \text{ of } P = 900$ ). Thus, $P = \frac{900}{20} \times 100 = 4500$ .

📐MAMath SolutionDirect Formula

📋 Given

Simple Interest (SI) = 900 rupees, Time (T) = 4 years, Rate (R) = 5% per annum.

🔢 Formula Used

P=SI×100R×TP = \frac{SI \times 100}{R \times T}P=R×TSI×100​

⚡ Exam Hall Shortcut / Speed Trick

Calculate the total percentage interest ( $R \times T = 5 \times 4 = 20\%$ ) and equate it to the interest amount ( $20\% \text{ of } P = 900$ ). Thus, $P = \frac{900}{20} \times 100 = 4500$ .

⚠️ Common Student Trap / Pitfall

Many students mistakenly multiply the rate by 100 or use the Compound Interest formula ( $A = P(1 + R/100)^T$ ) instead of the Simple Interest formula.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Identify Given Values

List the known variables: $SI = 900$ , $T = 4 \text{ years}$ , $R = 5\%$ .

SI=900,T=4,R=5SI = 900, T = 4, R = 5SI=900,T=4,R=5

Set up the formula

The formula for simple interest is $SI = (P \times R \times T) / 100$ . To find the principal $P$ , rearrange it to $P = (SI \times 100) / (R \times T)$ .

P=900×1005×4P = \frac{900 \times 100}{5 \times 4}P=5×4900×100​

Perform Calculation

Simplify the denominator $5 \times 4 = 20$ . Divide $900$ by $20$ to get $45$ , then multiply by $100$ .

P=9000020=4500P = \frac{90000}{20} = 4500P=2090000​=4500

✅

B is correct because the principal sum calculated using the formula is 4500.

Core Concepts Used

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Simple Interest calculation Algebraic transposition Percentage-to-decimal conversion

💡 EXAM TIP

This logic is the foundation for Profit and Loss percentages and Time-Value of Money concepts used in advanced Quantitative Aptitude.

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