Simple interest on a certain sum is 16/25 of the sum. The rate per cent, if the rate per cent and time (in years) are equal, is [SSC (CGL) 2011] |
A) 6%
B) 8%
C) 10%
D) 12%
Correct Answer: B
Solution :
Let the sum, \[P=x\] |
Then, \[SI=\frac{16}{25}x\]and \[t=r\] [given] |
By the formula, \[SI=\frac{P\times r\times t}{100}\] |
\[\Rightarrow \] \[\frac{16}{25}x=\frac{x\times r\times t}{100}\] |
\[\Rightarrow \] \[{{r}^{2}}=64\]\[\Rightarrow \]\[r=64\] |
\[\Rightarrow \] \[r=8%\]per annum |
Alternate Method |
If SI is \[\frac{x}{y}\]part of the principal P at the rate of r% per annum in \[t\,\,yr,\]also \[t=r\] |
Then, \[t=r=\sqrt{\frac{x}{y}\times 100}\] |
Here, \[\frac{x}{y}=\frac{16}{25}\] |
\[\Rightarrow \] \[r=\sqrt{\frac{16}{25}\times 100}\] |
\[=\sqrt{64}=8\]%per annum |
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