On a certain sum, the difference between the compound interest and the simple

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On a certain sum, the difference between the compound interest and the simple interest for the second year is Rs.4500 and the same for the third year is Rs.14175. What is the sum?

Answer: Option A
:
A

The difference in the SI and CI for the second year $= \frac{P r^{2}}{100^{2}} = 4500.................... (i)$
The difference in the SI and CI for the third year $= \frac{P r^{2}}{100^{2}} (3 + \frac{r}{100}) = 14175........... (i i)$
From the equation (i) and (ii).
$4500 \times (3 + \frac{r}{100}) = 14175$
$\frac{r}{100} = (\frac{14175}{4500} - 3)$
$r = \frac{675}{45} .$ Now ,from equation (i)
$P = \frac{4500}{r^{2}} \times 100^{2} \Rightarrow P = \frac{4500}{675 \times 675} \times 100^{2} \times 45 \times 45 \Rightarrow P = 2, 00, 000.$

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