What sum of money will yield 900 as simple interest in 3 years... | Mathematics MCQ | Examoogle

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MathematicsSimple & Compound Interest

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What sum of money will yield 900 as simple interest in 3 years at 6% per annum?

5000

4500

6000

5500

Correct Answer

📐 MA • Math Direct FormulaMathematicsSimple & Compound Interest

Option A

5000

Quick Summary:

Calculate the total percentage interest ( $R \times T = 6\% \times 3 = 18\%$ ) and equate 18% to 900. Since $18 \times 5 = 90$ , then $18 \times 500 = 9000$ , so 1% = 50 and 100% = 5000.

📐MAMath SolutionDirect Formula

📋 Given

Simple Interest (SI) = 900, Time (T) = 3 years, Rate of Interest (R) = 6% 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 ( $R \times T = 6\% \times 3 = 18\%$ ) and equate 18% to 900. Since $18 \times 5 = 90$ , then $18 \times 500 = 9000$ , so 1% = 50 and 100% = 5000.

⚠️ Common Student Trap / Pitfall

Confusing the simple interest formula with the compound interest formula by trying to apply $A = P(1 + \frac{R}{100})^n$ .

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Identify given variables

We are given $SI = 900$ , $T = 3$ years, and $R = 6\%$ .

SI=900,T=3,R=6SI = 900, T = 3, R = 6SI=900,T=3,R=6

State the formula

The standard simple interest formula is $SI = \frac{P \times R \times T}{100}$ . Rearranging to find the principal $P$ :

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

Substitute and solve

Substitute the values into the rearranged formula: $P = \frac{900 \times 100}{6 \times 3}$ . Calculating the denominator: $6 \times 3 = 18$ . Dividing 900 by 18 gives 50, then multiplying by 100 results in 5000.

P=900×10018=50×100=5000P = \frac{900 \times 100}{18} = 50 \times 100 = 5000P=18900×100​=50×100=5000

✅

A is correct because the principal amount required to earn 900 as simple interest at 6% over 3 years is exactly 5000.

Core Concepts Used

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Simple Interest Principal Calculation Algebraic Manipulation

💡 EXAM TIP

This concept is fundamental for Profit and Loss and Time, Speed, and Distance problems, where interest is analogous to distance and the rate/time relationship acts similarly to speed/time.

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