Question

The compound interest on a certain sum of money at 16 2/3 % after 2 years is rs 585. find the simple interst on the same sum of money at the same rate after 3 years

Answer 1

hope the answer is correct

Answer 2

$Let \: the \:sum(Principal ) = P$

$Rate \:of \: interest (R) = 16\frac{2}{3}\% \\= \frac{50}{3}\%\: p.a$

$Time (T) = 2 \: years$

$Conversion \:period (n) = 2$

$i ) Compound \: interest (c.i) = Rs \:585\:(given)$

$\implies \pink {P[ \Big( 1 + \frac{R}{100} \Big)^{2} - 1] = 585}$

$\implies P[\Big( 1 + \frac{\frac{50}{3}}{100}\Big)^{2} - 1] = 585$

$\implies P[\Big( 1 + \frac{1}{6}\Big)^{2} - 1] = 585$

$\implies P[\Big(\frac{ 6 + 1}{6}\Big)^{2} - 1] = 585$

$\implies P[\Big(\frac{7}{6}\Big)^{2} - 1] = 585$

$\implies P\Big(\frac{49}{36} - 1\Big)= 585$

$\implies P\Big(\frac{49-36}{36} \Big)= 585$

$\implies P\Big(\frac{13}{36} \Big)= 585$

$\implies P = 585 \times \frac{36}{13}$

$\implies P = 45 \times 36$

$\implies P = Rs \: 1620\: --(1)$

$ii ) Now, Sum (P) = Rs \:1620$

$Rate \:of \: interest (R) = 16\frac{2}{3}\% \\= \frac{50}{3}\%\: p.a$

$Time (T) = 3 \: years$

$\boxed { \pink { Simple \: interest = \frac{PTR}{100} }}$

$\implies S.I = \frac{ 1620 \times3 \times \frac{50}{3}}{100} \\= \frac{ 1620 \times 50}{ 100} \\= 162 \times 5 \\= Rs \:810$

Therefore.,

$\red { Required \:sum }\green {= Rs \:1620}$

$\red {S.I }\green {= Rs \: 810 }$

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