Question

A sum of money lent out at simple interest amounts to rs 5000 in 2 yrs and rs 11000in 5 yrs. Find the sum of money and rate of interest. ​

Answer 1

$i) Let \:the \:sum \:lent (Principal) = Rs \:x$

$Let \:rate \:of \: interest = R$

$Time (T) = 2 \:years$

$Amount = Rs \: 5000$

$\boxed { \pink { A = P\Big( 1 + \frac{RT}{100} \Big) }}$

$\implies 5000 = x\Big( 1 + \frac{2R}{100}\Big)\:--(1)$

$ii) Let \:the \:sum \:lent (Principal) = Rs \:x$

$Let \:rate \:of \: interest = R$

$Time (T) = 5 \: years$

$Amount = Rs \: 11000$

$\implies 5000 = x\Big( 1 + \frac{5R}{100}\Big)\:--(2)$

$Do \: (2) \div (1) ,\:we \:get$

$\implies \frac{11}{5} = \frac{\Big( 1 + \frac{5R}{100}\Big) }{\Big( 1 + \frac{2R}{100}\Big) }$

$\implies 11\Big( 1 + \frac{2R}{100}\Big) = 5\Big( 1 + \frac{5R}{100}\Big)$

$\implies 11 + \frac{22R}{100} = 5+ \frac{25R}{100}$

$\implies 11 - 5 = \frac{25R}{100} - \frac{22R}{100}$

$\implies 6 = \frac{3R}{100}$

$\implies 6 \times \frac{100}{3} = R$

$\implies R = 200\%$

/* Now ,Put value of R , in equation (1) ,we get */

$5000 = x \Big( 1 + \frac{2\times 200}{100}\Big)$

$\implies 5000 = x \Big( 1 + 4\Big)$

$\implies 5000 = 5x$

$\implies x = \frac{5000}{5}$

$\implies x = Rs \:1000$

Therefore.,

$\red { Money \:lent } \green { = Rs \:1000}$

$\red { Rate \:of \: interest } \green {= 200\% }$

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