A sum of money doubles itself in 8 years at simple interest. I... | Mathematics MCQ | Examoogle

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A sum of money doubles itself in 8 years at simple interest. In how many years will it become four times itself?

16 years

20 years

24 years

32 years

Correct Answer

📐 MA • Math Direct FormulaMathematicsSimple & Compound Interest

Option C

24 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. Here, $T_1 = 8$ , $n_1 = 2$ , and $n_2 = 4$ .

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📐MAMath SolutionDirect Formula

📋 Given

A sum of money doubles itself in 8 years under Simple Interest. We need to find the time required for it to become 4 times itself.

🔢 Formula Used

T2=T1×n2−1n1−1T_2 = T_1 \times \frac{n_2 - 1}{n_1 - 1}T2​=T1​×n1​−1n2​−1​

⚡ 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. Here, $T_1 = 8$ , $n_1 = 2$ , and $n_2 = 4$ .

⚠️ Common Student Trap / Pitfall

Many students mistakenly assume that if it doubles in 8 years, it will quadruple in 16 years, forgetting that interest is earned only on the initial principal, not on the total accumulated amount.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Calculate the Interest Rate

If the sum $P$ becomes $2P$ in 8 years, the Simple Interest earned is $I = 2P - P = P$ . Using the formula $I = \frac{P \times R \times T}{100}$ , we get $P = \frac{P \times R \times 8}{100}$ .

R=1008=12.5%R = \frac{100}{8} = 12.5\%R=8100​=12.5%

Set target conditions

For the money to become 4 times itself, the total amount $A$ must be $4P$ . Therefore, the Simple Interest required is $I = 4P - P = 3P$ .

I=3PI = 3PI=3P

Calculate the time

Substitute $I = 3P$ and $R = 12.5$ into the formula $T = \frac{100 \times I}{P \times R}$ .

T=100×3PP×12.5=30012.5=24T = \frac{100 \times 3P}{P \times 12.5} = \frac{300}{12.5} = 24T=P×12.5100×3P​=12.5300​=24

✅

C is correct because the simple interest grows linearly, requiring 8 years to gain 100% of the principal, and thus 24 years to gain 300% (triple the interest).

Core Concepts Used

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Simple Interest Principle Linear Growth of Interest Multiplier Formula

💡 EXAM TIP

This concept is identical to solving problems involving arithmetic progression where the common difference is the annual interest earned on the initial principal.

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