ஒரு குறிப்பிட்ட தொகைக்கு, அதே வட்டி விகிதத்தில், 2 ஆண்டுகளுக்க... | Mathematics MCQ (தமிழ்) | Examoogle

MathematicsSimple & Compound Interest

ஒரு குறிப்பிட்ட தொகைக்கு, அதே வட்டி விகிதத்தில், 2 ஆண்டுகளுக்கு தனி வட்டி ₹66 மற்றும் கூட்டு வட்டி ₹69. அசல் தொகை (₹ இல்) என்ன?

358

356

367

363

Correct Answer

📐 MA • Math Direct FormulaMathematicsSimple & Compound Interest

358

Quick Summary:

The interest on interest for the second year is $CI - SI = 69 - 66 = 3$ . This ₹3 is the interest on the first year's simple interest (₹33) at the same rate. Thus, $r = (3/33) \times 100 = 9.09\%$ . Apply this to find P.

📐MAMath SolutionDirect Formula

📋 Given

Simple Interest (SI) for 2 years = ₹66, Compound Interest (CI) for 2 years = ₹69.

🔢 Formula Used

Rate(r)=2(CI−SI)SI×100\text{Rate} (r) = \frac{2(CI - SI)}{SI} \times 100Rate(r)=SI2(CI−SI)​×100 and Sum(P)=SI×100r×T\text{Sum} (P) = \frac{SI \times 100}{r \times T}Sum(P)=r×TSI×100​

⚡ Exam Hall Shortcut / Speed Trick

⚠️ Common Student Trap / Pitfall

Many students mistake the 2-year SI as the interest for only one year; remember that SI is the same for every year, so $SI_{1year} = 66 / 2 = 33$ .

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Calculate SI for one year

Since Simple Interest is uniform for each year, the interest for one year is half of the total simple interest for two years.

SI1yr=662=33SI_{1yr} = \frac{66}{2} = 33SI1yr​=266​=33

Find the interest earned on interest

The difference between Compound Interest and Simple Interest for two years is the interest earned on the first year's interest.

Diff=CI−SI=69−66=3\text{Diff} = CI - SI = 69 - 66 = 3Diff=CI−SI=69−66=3

Calculate the rate of interest

The interest of ₹3 is earned on the base of ₹33 at the rate 'r' for one year.

r=333×100=10011≈9.09%r = \frac{3}{33} \times 100 = \frac{100}{11} \approx 9.09\%r=333​×100=11100​≈9.09%

Determine the principal sum

Substitute the rate and the 1-year SI into the Simple Interest formula: $SI = (P \times r \times T) / 100$ .

33=P×(100/11)×1100  ⟹  P=33×11=36333 = \frac{P \times (100/11) \times 1}{100} \implies P = 33 \times 11 = 36333=100P×(100/11)×1​⟹P=33×11=363

✅

D is correct because calculating the rate from the CI-SI difference and substituting it into the SI formula yields the principal sum of ₹363.

Core Concepts Used

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Simple Interest Compound Interest Difference of SI and CI

💡 EXAM TIP

This concept is a subset of the 'Successive Percentage' topic; $CI - SI$ for 2 years is equivalent to $P \times (r/100)^2$ .

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