Question

A person had rs.8400. he lent a part of it at 4% and the remaining at 3 (1/3) % simple interest. his total annual income was rs.294. find the sum he lent at 4%.

Answer 1

$Total \: amount \: a \: person \:had = Rs \:8400$

Case 1:

$Let \: the \: sum \: lent = Rs \: x$

$Rate \:of \: Interest (R) = 4\%$

$Time (T) = 1 \:year$

$Simple \: Interest (I_{1}) = \frac{PTR}{100} \\= \frac{x \times 1 \times 4 }{100}\\= \frac{4x}{100} \: --(1)$

Case 2:

$Remaining \: sum \: lent = Rs \: ( 8400-x)$

$Rate \:of \: Interest (R) = 3\frac{1}{3}\% \\= \frac{10}{3}\%$

$Time (T) = 1 \:year$

$Simple \: Interest (I_{2}) = \frac{PTR}{100} \\= \frac{(8400-x) \times 1 \times \frac{10}{3}}{100}\\= \frac{(84000- 10x)}{300} \: --(2)$

/* According to the problem given */

$Total \: annual \: Interest = Rs \:294$

$\implies I_{1} + I_{2} = 294$

$\implies \frac{4x}{100} + \frac{84000-10x}{300} = 294$

$\implies \frac{ 12x + 84000 - 10x}{300} = 294$

$\implies 2x + 84000 = 294 \times 300$

$\implies 2x = 88200 - 84000$

$\implies 2x = 4200$

$\implies x = \frac{4200}{2}$

$\implies x = 2100$

Therefore.,

$\red {The \:sum \:he: lent: at 4\%.}\green {= Rs\:2100}$

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