The difference between CI and SI on a certain sum of money at 623- p-a- for 3 years is Rs- 46- Find the sum-

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Standard XII

Mathematics

Infinite GP

The differenc...

Question

The difference between CI and SI on a certain sum of money at $6 \frac{2}{3} %$ p.a. for $3$ years is Rs. $46$ . Find the sum.

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Solution

$C I = P [{(1 + r)}^{n} - 1]$
P = principle amount
r = rate per period
n = number of periods
SI = prt
P = principle amount
r = rate
t = time
$\begin{matrix} C I - S I = P [{(1 + r)}^{n} - 1 - r t] 46 = P [{(1 + \frac{20}{300})}^{3} - 1 - \frac{20}{300} \times 3] 46 = P [{(\frac{16}{15})}^{3} - 1 - \frac{1}{5}] [P = 38 r s] \end{matrix}$

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The difference between CI and SI on a certain sum of money at 623% p.a. for 3 years is Rs. 46. Find the sum.

CI=P[(1+r)n−1]P = principle amountr = rate per periodn = number of periodsSI = prtP = principle amountr = ratet = timeCI−SI=P[(1+r)n−1−rt]46=P[(1+20300)3−1−20300×3]46=P[(1615)3−1−15][P=38rs]

The difference between CI and SI on a certain sum of money at $6 \frac{2}{3} %$ p.a. for $3$ years is Rs. $46$ . Find the sum.