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Question
The difference between the compound interest and simple interest on a certain sum at 15% per annum for 3 years is Rs 283.50. Find the sum.
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Solution
Given:
CI - SI = Rs 283 . 50
R = 15 %
n = 3 years
Let the sum be Rs x.
We know that:
\[A = P(1 + \frac{R}{100} )^n \]
\[ = P(1 + \frac{R}{100} )^n \]
\[ = x(1 + \frac{15}{100} )^3 \]
\[ = x \left( 1 . 15 \right)^3 . . . (1)\]
Also,
\[SI = \frac{PRT}{100} = \frac{x(15)(3)}{100} = 0 . 45 x\]
\[A = SI + P = 1 . 45x . . . (2)\]
Thus, we have:
\[x \left( 1 . 15 \right)^3 - 1 . 45x = 283 . 50 \][From (1) and (2)]
\[1 . 523x - 1 . 45x = 283 . 50\]
\[0 . 070875x = 283 . 50\]
\[x = \frac{283 . 50}{0 . 070875}\]
\[ = 4, 000\]
Thus, the sum is Rs 4, 000.
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