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What will be the difference between S.I. and C.I. on a sum of Rs. 15000 for 2 years at the same rate of interest of 12(1/2) % per annum ?

What will be the difference between S.I. and C.I. on a sum of Rs. 15000 for 2 years at the same rate of interest of $$12\frac{1}{2}$$ % per annum ?
a) Rs. 230.550
b) Rs. 234.375
c) Rs. 250.129
d) Rs. 324.357

Answer: b
Explanation:
$$\eqalign{ & {\text{S}}{\text{.I}}{\text{. = Rs}}{\text{. }}\left( {15000 \times \frac{{25}}{2} \times 2 \times \frac{1}{{100}}} \right) \cr & \,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}3750 \cr & {\text{C}}{\text{.I}}{\text{. = Rs}}{\text{. }}\left[ {15000{{\left( {1 + \frac{{25}}{{2 \times 100}}} \right)}^2} – 15000} \right] \cr & = {\text{Rs}}{\text{. }}\left( {15000 \times \frac{9}{8} \times \frac{9}{8} – 15000} \right) \cr & = {\text{Rs}}{\text{. }}\left( {18948.375 – 15000} \right) \cr & = {\text{Rs}}{\text{. }}3984.375 \cr & {\text{Difference }}{\text{ = Rs}}{\text{. }}\left( {3984.375 – 3750} \right) \cr & = {\text{Rs}}{\text{. }}234.375 \cr} $$

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