Question

Rekhadidi deposited RS 10000 of her savings in two separate banks at the same time. The rate of simple interest per annum is 6% in one bank and 7% in another bank ; after 2 yr., if she gets RS 1280 in total as interest, then let us write by calculating, the sums of money she had deposited separately in each of the two banks.

Answer 1

$Deposited \: amount (A) = Rs \:10000$

Case 1:

$Principal \: in \:first \:bank = Rs \:x \\Rate \:of \: Interest (R) = 6\% , \\Time (T) = 2\: years$

$Simple \: interest (I_{1}) = \frac{PTR}{100} \}= \frac{x \times 6 \times 2 }{100} \\= \frac{6x}{50} \:---(1)$

Case 2:

$Principal \: in \:Second \:bank = Rs \:(10000-x) \\Rate \:of \: Interest (R) = 7\% , \\Time (T) = 2\: years$

$Simple \: interest (I_{2}) = \frac{PTR}{100} \}= \frac{(10000-x) \times 7 \times 2 }{100} \\= \frac{7(10000-x)}{50} \:---(2)$

/ * According to the problem given */

$Total \: interest = Rs \: 1280$

$\implies \frac{6x}{50} + \frac{7(10000-x)}{50}= 1280 \: [ From \:(1) \:and\: (2) ]$

$\implies \frac{6x+7(10000-x)}{50} = 1280$

$\implies 6x + 70000 - 7x = 64000$

$\implies 70000 - 64000 = 7x - 6x$

$\implies 6000 = x$

Therefore.,

$Principal \: in \: first \: bank = x = Rs \:6000$

$Principal \: in \: Second \: bank = (10000 - x)\\ = Rs \:10000 - Rs \:6000\\= Rs \: 4000$

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Answer 2

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