1000 Rs. is invested at 5% per annum simple interest. If the interest is added to the principal after every 10 years, the amount will become 2000 Rs. after :

1000 Rs. is invested at 5% per annum simple interest. If the interest is added to the principal after every 10 years, the amount will become 2000 Rs. after :
[A]$latex 15\ years$
[B]$latex 16\frac{2}{3}\ years&s=1$
[C]$latex 18\ years$
[D]$latex 20\ years$

$latex \mathbf{16\frac{2}{3}}\ years&s=1$
After 10 years
$latex SI = \frac{1000\times 5\times 10}{100} = 500\ Rs.&s=1$
Principal for 11th year = 1000 + 500 = 1500 Rs.
$latex \therefore T = \frac{SI\times 100}{P\times R} = \frac{500\times 100}{1500\times 5}&s=1$
$latex = \frac{20}{3}\ years = 6\frac{2}{3}\ years&s=1$
∴ Total time $latex = 10+6\frac{2}{3} = 16\frac{2}{3}\ years&s=1$
Hence option [B] is correct answer.


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