Question

Rs. $1000$ invested at $5\%$ p.a simple interest, if the interest is added to the principle after every $10$ years, the amount will become Rs. $2000$ after

• A. $15$ years
• B. $16\frac{2}{3}$ years
• C. $18$ years
• D. $20$ years

Answer 1

The correct option is B $16\frac{2}{3}$ years

S.I. for $10$ years $=$ Rs $(1000\times \frac{5}{100}\times 10)=$ Rs. $500$
Principal after $10$ years becomes $=$ Rs. $(1000+500)=$ Rs. $1500$.
Amount on that principal after $t$ years $=$ Rs. $2000$
$\therefore$ S.I. on it $=$ Rs. $(2000-1500)=$ Rs. $500$
$\therefore t=\left(\frac{500\times 100}{1500\times 5}\right)$ years $=6\frac{2}{3}$ years
$\therefore$ Total time $=$ $(10+6\frac{2}{3})$ years $=16\frac{2}{3}$ years