A sum of money doubles itself in 5 years at simple interest. I... | Mathematics MCQ | Examoogle

Examoogle • User • info@examoogle.com • EE-2024-8821

Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked

MathematicsSimple & Compound Interest

A sum of money doubles itself in 5 years at simple interest. In how many years will it become 4 times the original amount?

10 years

12 years

15 years

20 years

Correct Answer

📐 MA • Math Direct FormulaMathematicsSimple & Compound Interest

Option C

15 years

Quick Summary:

Use the formula $T_2 = T_1 \times \frac{(n_2 - 1)}{(n_1 - 1)}$ , where $n$ is the multiplier of the principal.

🎯

Crack Simple & Compound Interest with Examoogle SuperTeachers

Get Free Demo Classes & Live Mocks →

📐MAMath SolutionDirect Formula

📋 Given

A sum of money doubles itself in 5 years at simple interest. We need to find the time taken for it to become 4 times the original amount.

🔢 Formula Used

SI=P×R×T100SI = \frac{P \times R \times T}{100}SI=100P×R×T​

⚡ Exam Hall Shortcut / Speed Trick

Use the formula $T_2 = T_1 \times \frac{(n_2 - 1)}{(n_1 - 1)}$ , where $n$ is the multiplier of the principal.

⚠️ Common Student Trap / Pitfall

Many students mistake 'becomes 4 times' for 'interest is 4 times'. Always remember that $\text{Amount} = \text{Principal} + \text{Interest}$ , so for 4 times the amount, the interest is $3P$ .

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Analyze the first condition

If the sum doubles, Amount = $2P$ . Therefore, Simple Interest $SI = 2P - P = P$ . Given time $T_1 = 5$ years.

P=P×R×5100  ⟹  R=20%P = \frac{P \times R \times 5}{100} \implies R = 20\%P=100P×R×5​⟹R=20%

Analyze the second condition

We want the sum to become 4 times, so Amount = $4P$ . Therefore, Simple Interest $SI = 4P - P = 3P$ . We need to find $T_2$ using the rate $R = 20\%$ .

3P=P×20×T21003P = \frac{P \times 20 \times T_2}{100}3P=100P×20×T2​​

Solve for T2

Solving for $T_2$ : $3P = \frac{P \times T_2}{5}$ , which simplifies to $T_2 = 3 \times 5 = 15$ .

T2=15 yearsT_2 = 15 \text{ years}T2​=15 years

✅

C is correct because for the money to become 4 times, the interest earned must be 3 times the principal, which requires 3 times the duration required to earn 1 time the principal as interest.

Core Concepts Used

Click any tag to open in AI Tutor

Simple Interest calculation Amount vs Interest relationship Time-multiplication proportionality

💡 EXAM TIP

This ratio method works for any multiple-sum problem in simple interest; remember that the interest portion is always $n-1$ times the principal.

Was this solution helpful?

⚡ Practice on Android App · 4.8 ★

Solve 10,000+ More Questions with AI Tutor

Get instant step-by-step AI explanations, full shift Previous Year Papers (SSC GD, RRB, SSC JE), and regional rank analysis on the official Examoogle App.

Free Download • 100K+ Aspirants

Discussion (0)

Loading discussion...

Prev Next

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Related Questions

Discussion (0)