Simple interest on a certain amount is $$\frac{9}{{16}}$$ of the principal. If the numbers representing the rate of interest in percent and time in years be equal, then time, for which the principal is lent out, is -
A. $$5\frac{1}{2}$$ years
B. $$6\frac{1}{2}$$ years
C. 7 years
D. $$7\frac{1}{2}$$ years
Answer: Option D
Solution(By Examveda Team)
$$\eqalign{ & {\text{Let}}\,{\text{sum}} = x. \cr & {\text{Then,}} \cr & {\text{S}}{\text{.I}}{\text{.}} = \frac{{\text{9}}}{{{\text{16}}}}x \cr & {\text{Let rate}} = {\text{R}}\% \,\text{and} \cr & \text{time} = R\,\text{years} \cr & \therefore \left( {\frac{{x \times {\text{R}} \times {\text{R}}}}{{100}}} \right) = \frac{{9x}}{{16}} \cr & \Rightarrow {{\text{R}}^2} = \frac{{900}}{{16}} \cr & {\text{R}} = \frac{{30}}{4} = 7\frac{1}{2} \cr & {\text{Hence,}} \cr & {\text{time}} = 7\frac{1}{2}\text{years} \cr} $$Related Questions on Interest
Find the simple interest on Rs. 5200 for 2 years at 6% per annum.
A. Rs. 450
B. Rs. 524
C. Rs. 600
D. Rs. 624
Rs. 1200 is lent out at 5% per annum simple interest for 3 years. Find the amount after 3 years.
A. Rs. 1380
B. Rs. 1290
C. Rs. 1470
D. Rs.1200
E. Rs. 1240
Interest obtained on a sum of Rs. 5000 for 3 years is Rs. 1500. Find the rate percent.
A. 8%
B. 9%
C. 10%
D. 11%
E. 12%
Rs. 2100 is lent at compound interest of 5% per annum for 2 years. Find the amount after two years.
A. Rs. 2300
B. Rs. 2315.25
C. Rs. 2310
D. Rs. 2320
E. None of these
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