susan invested certain amount of money in 2 schemes A and B which offer interest at the rate of 8%per annum and 9% per annum. she received rupees 1860 as annual interest. however had she interchanged the amount of investment in 2 schemes she would have received rupees 20 more as annual interest. how much money did she invest in each schemes??
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Answers
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
Answer: 12000 Rs and 10000 RS respectively
Explanation: Refer image
