Question

Susan invested certain amount of money in the schemes A and B which offered interest at the rate of 8% per annum and 9% per annum respectively. She received Rs.1860 as annual interest. However , had she interchanged the amount of investment in two schemes she would have received Rs.20 more as annual interest.How much money did she invested in each scheme?

Answer ASAP...​

Answer 1

Given: Scheme A & B : Rate of interest - 8% and 9% respectively

Annual interest received - Rs.1,860/- i.e. interest @ 8% on scheme A + interest @ 9% on scheme B = Total amount received

If the investment was interchanged, then he would receive Rs.20 more as annual interest.

Assume investment he made as x & y respectively.

Now, from the given, it can be said that

Simple interest =\frac{p R T}{100}.

So,

x \times 8 \times \frac{1}{100}+y \times 9 \times \frac{1}{100}=1860

8 \mathrm{x}+9 \mathrm{y}=186000 \quad \dots \ldots \ldots \ldots(1)

If the amount is interchanged, then

x \times 9 \times \frac{1}{100}+y \times 8 \times \frac{1}{100}=1860+20

\frac{9 x}{100}+\frac{8 y}{100}=1880

9 \mathrm{x}+8 \mathrm{y}=188000 \ldots \ldots \ldots \ldots(2)

Multiply (1) by 9 and (2) by 8 i.e.

9 to be multiplied with 8x + 9y = 186000

8 to be multiplied with 9x + 8y = 188000, we get

72x + 81y = 1674000

72x + 64y = 1504000

Subtracting both the equations, we get

17y = 170000

y = 10000

Now, substituting y = 10000 in 8x + 9y = 186000,

8x + 90000 = 186000

8x = 186000-90000

8x = 96000

x = 12000

Hence, the amount of investment in Scheme A & B is Rs.12000 & 10000

Answer 2

We will take simple interest given that the type of accumulation is not specified.

The period for the two investments is 1 year.

Let us take A:

i = 8%

let amount be x.

Simple interest = Principle × rate/100 time

Interest = 0.08 × 1 × x = 0.08x

Lets take B:

let Principle of B be y.

Interest = 0.09y

The equation is :

0.08x + 0.09y = 1860

If we interchange we will have :

0.09x + 0.08y = (1860 + 20)

0.09x + 0.08y = 1880

Solving for x and y simultaneously:

0.08x + 0.09y = 1860...............1)

0.09x + 0.08y = 1880................2)

Multiply 1 by 9 and 2 by 8 to eliminate x.

0.72x + 0.81y = 16740

0.72x + 0.64y = 15040

Subtraction:

0.17y = 1700

y = 10000

Doing the substitution:

0.08x + 0.09(10000) = 1860

0.08x = 1860 - 900

0.08x = 960

x = 960/0.08

x = 12000

The amounts are :

10000 in A and 12000 in B