If the interest earned during the 2nd year on a certain sum is... | Stage I (CBT I) MCQ | Examoogle

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Stage I (CBT I)RRB ALP CBT-I 11 Mar, 2026 Shift 1

If the interest earned during the 2nd year on a certain sum is ₹6330, and the rate of interest is 20% per annum compounded annually, then the sum is:

₹25465

₹26160

₹26375

₹25850

Correct Answer

📚 GK • GK Ratio MethodStage I (CBT I)RRB ALP CBT-I 11 Mar, 2026 Shift 1

Option C

₹26375

Quick Summary:

Given: Interest earned during the 2nd year = ₹6330, Rate of interest (R) = 20% per annum compounded annually.

📐MAMath SolutionRatio Method

📋 Given

Interest earned during the 2nd year = ₹6330, Rate of interest (R) = 20% per annum compounded annually.

🔢 Formula Used

Interest in 2nd year=P×(1+R100)1×R100\text{Interest in 2nd year} = P \times \left(1 + \frac{R}{100}\right)^1 \times \frac{R}{100}Interest in 2nd year=P×(1+100R​)1×100R​

⚡ Exam Hall Shortcut / Speed Trick

At 20% per annum, 1st year interest = 20% of Principal ( $P$ ). 2nd year interest includes 20% on principal plus 20% interest on 1st year's interest ( $20\% + 20\% \text{ of } 20\% = 24\%$ of $P$ ). Thus, $24\% \text{ of } P = 6330 \implies P = \frac{6330}{24} \times 100 = ₹26,375$ .

⚠️ Common Student Trap / Pitfall

Confusing 'interest earned in 2nd year' with total compound interest earned after 2 years. Using $CI_2 = P[(1+r/100)^2 - 1] = 0.44P$ instead of $0.24P$ leads to an incorrect principal of ₹14,386.36.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Understand Interest Earned Specifically in 2nd Year

Let the Principal sum be $P$ . In compound interest, the principal for the $2°{\text{nd}}$ year is the amount accumulated at the end of the $1°{\text{st}}$ year, which is $A_1 = P \left(1 + \frac{R}{100}\right)$ .

A1=P(1+20100)=1.2PA_1 = P \left(1 + \frac{20}{100}\right) = 1.2PA1​=P(1+10020​)=1.2P

Express 2nd Year Interest in terms of Principal

The interest earned during the $2°{\text{nd}}$ year alone is $20\%$ of $A_1$ :

Interest2nd year=A1×20100=1.2P×0.20=0.24P\text{Interest}_{2\text{nd year}} = A_1 \times \frac{20}{100} = 1.2P \times 0.20 = 0.24PInterest2nd year​=A1​×10020​=1.2P×0.20=0.24P

Set up Equation with Given Value and Solve for P

We are given that the $2°{\text{nd}}$ year interest is $₹6330$ . Equating $0.24P = 6330$ :

P=63300.24=6330×10024=₹26,375P = \frac{6330}{0.24} = \frac{6330 \times 100}{24} = ₹26,375P=0.246330​=246330×100​=₹26,375

✅

C is correct because calculating the principal from 24% of the sum equal to ₹6330 gives ₹26,375.

Core Concepts Used

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Compound Interest Year-wise Breakdown Effective Rate of Interest Percentage-to-Principal Ratio Method

💡 EXAM TIP

For compound interest problems involving specific individual years (like $2°{\text{nd}}$ or $3°{\text{rd}}$ year), convert the rate into a fraction (e.g., $20\% = 1/5$ ) and assume a principal as a multiple of $5°t$ to perform quick integer calculations without decimals.

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