Question

a man invested certain amount of money in two schemes A and B which offer interest at the rate of 8% per annum and 9% per annum respectively. he received ₹1860 as annual interest . however , if he had interchanged the amount of investment in the two schemes he would have received₹20 more as annual interest. how much money did he invest in each scheme?

Answer 1

I know this is not the interest method but maybe this would help U

Answer 2

He invest in Scheme A = Rs.12,000 & Scheme B = Rs.10,000.

To find:

Amount of investment in Scheme A & Scheme B

Solution:

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.