Question

. Kavya deposits her total sum,
partly in
scheme A and partly in scheme B. The rate
of interest in scheme A is 8% p.a. and the
rate of interest in scheme B is 9 % p.a. At
the end of the year, she received Rs.1860 as
total interest. If she interchanges the amounts
invested in scheme A and scheme B, she
would receive Rs.20 more interest. Find her
investments in both the schemes.

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Answer 1

AnSwer :-

According to the simple interest methods,

The period for the two investments is 1 year(P.A)

Firstly, let us take the 1st case, that is, A,

i = 8%

let the amount be x.

$\sf \: Simple \: interest = Principle \times \dfrac{rate}{100}$

$\implies \sf \: 0.08 \times 1 \times x\\ \implies \sf \: 0.08x$

Now the 2nd case, that is, B.

Let Principle of B be y.

$\sf \: Simple \: interest = Principle \times \dfrac{rate}{100}$

$\implies \sf \: 0.09 \times 1 \times y \\ \implies \sf \: 0.09y$

Now subtracting these,

$\implies \sf \: 0.17y = 1700 \\ \implies \sf \: y = 10000$

Equation becomes,

$\implies \sf \: 0.08x + 0.09y = 1860$

If we will interchange these equations,

$\implies \sf \: 0.09x + 0.08y = (1860 + 20) \\\implies \sf \: 0.09x + 0.08y = 1880$

Solving for x and y respectively,

$\implies \sf \: 0.08x + 0.09y = 1860 \\ \implies \sf \:0.09x + 0.08y = 1880$

★Multiply 1 by 9 and 2 by 8 to eliminate x :-

$\implies \sf \:0.08x + 0.09y = 1860$

$\implies \sf \:0.09x + 0.08y = 1880$

Further on Subtraction :

$\implies \sf \: 0.17y = 1700 \\ \implies \sf \:y = 10000$

Again, by further the substitution:

$\implies \sf \: 0.08x + 0.09(10000) = 1860 \\ \implies \sf \:0.08x = 1860 - 900\\\implies \sf \:0.08x = 960 \\\implies \sf \:x = \frac{960}{0.08} \\ \implies \sf \: x = 12000$

★The amounts are :

10000 in A and 12000 in B.