Question : If INR 2,000 is invested at a simple interest rate of 5% per annum and the interest is added to the principal after 10 years, then in how many years will it amount to INR 4,000 at the same rate of interest?
Option 1: $18 \frac{2}{3}$ years
Option 2: $16 \frac{1}{3}$ years
Option 3: $16 \frac{2}{3}$ years
Option 4: $18 \frac{1}{3}$ years
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Correct Answer: $16 \frac{2}{3}$ years
Solution :
Simple interest for 10 years
= $\frac{\text{Principal × Rate × Time}{}}{100}$
= $\frac{\text{2000 × 5 × 10}{}}{100}$
= $1000$
Amount after 10 year = 2000 + 1000 = 3000
To get INR 4000 = 4000 – 3000 = 1000 is required.
$\therefore$ Simple interest = 1000
Principal becomes = 3000
Rate = 5%
Simple interest = $\frac{\text{Principal × Rate × Time}{}}{100}$
⇒ $1000 = \frac{\text{3000 × 5 × Time}{}}{100}$
⇒ Time $=\frac{20}{3}$ years
⇒ Time $=6 \frac{2}{3}$ years
Total time $= 10 + 6 \frac{2}{3}= 16 \frac{2}{3}$ years
Hence, the correct answer is $16 \frac{2}{3}$ years.
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