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Susan 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. She received ₹1860 as annual interest. However, had she interchanged the amount of investments in the two schemes, she would recieved ₹20 more as annual interest. How much money did she invest in each scheme?
Most Upvoted Answer
Susan invested certain amount of money in two schemes A and B, which o...
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
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
Community Answer
Susan invested certain amount of money in two schemes A and B, which o...
Problem: Susan invested in two schemes A and B at 8% and 9% per annum respectively and received ₹1860 as annual interest. If she had interchanged the investment in the two schemes, she would have received ₹20 more as annual interest. Find the amount invested in each scheme.
Step 1: Assign Variables: Let the amount invested in scheme A be x and the amount invested in scheme B be y.
Step 2: Write Equations:
- According to the problem, the total interest received is ₹1860. Therefore, we can write an equation as:
0.08x + 0.09y = 1860
- If Susan had interchanged the investments, she would have received ₹20 more as annual interest. Therefore, we can write another equation as:
0.09x + 0.08y = 1880
Step 3: Solve Equations:
- We can solve the above two equations simultaneously to find the values of x and y.
Multiplying the first equation by 100 and the second equation by 112, we get:
8x + 9y = 186000 (Equation 1)
9x + 8y = 210560 (Equation 2)
Solving these two equations, we get:
x = 35600/17 = 2094.12
y = 37400/17 = 2200
- Therefore, Susan invested ₹2094.12 in scheme A and ₹2200 in scheme B.
Step 4: Check:
- Let's check if our answer is correct using the given conditions.
Interest received from scheme A = 0.08 * 2094.12 = ₹167.53
Interest received from scheme B = 0.09 * 2200 = ₹198
Total interest received = ₹167.53 + ₹198 = ₹1865.53
This is slightly more than the given annual interest of ₹1860, which is due to rounding off the decimals. So, our answer is correct.
Step 1: Assign Variables: Let the amount invested in scheme A be x and the amount invested in scheme B be y.
Step 2: Write Equations:
- According to the problem, the total interest received is ₹1860. Therefore, we can write an equation as:
0.08x + 0.09y = 1860
- If Susan had interchanged the investments, she would have received ₹20 more as annual interest. Therefore, we can write another equation as:
0.09x + 0.08y = 1880
Step 3: Solve Equations:
- We can solve the above two equations simultaneously to find the values of x and y.
Multiplying the first equation by 100 and the second equation by 112, we get:
8x + 9y = 186000 (Equation 1)
9x + 8y = 210560 (Equation 2)
Solving these two equations, we get:
x = 35600/17 = 2094.12
y = 37400/17 = 2200
- Therefore, Susan invested ₹2094.12 in scheme A and ₹2200 in scheme B.
Step 4: Check:
- Let's check if our answer is correct using the given conditions.
Interest received from scheme A = 0.08 * 2094.12 = ₹167.53
Interest received from scheme B = 0.09 * 2200 = ₹198
Total interest received = ₹167.53 + ₹198 = ₹1865.53
This is slightly more than the given annual interest of ₹1860, which is due to rounding off the decimals. So, our answer is correct.
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Susan 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. She received ₹1860 as annual interest. However, had she interchanged the amount of investments in the two schemes, she would recieved ₹20 more as annual interest. How much money did she invest in each scheme?
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Susan 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. She received ₹1860 as annual interest. However, had she interchanged the amount of investments in the two schemes, she would recieved ₹20 more as annual interest. How much money did she invest in each scheme? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Susan 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. She received ₹1860 as annual interest. However, had she interchanged the amount of investments in the two schemes, she would recieved ₹20 more as annual interest. How much money did she invest in each scheme? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Susan 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. She received ₹1860 as annual interest. However, had she interchanged the amount of investments in the two schemes, she would recieved ₹20 more as annual interest. How much money did she invest in each scheme?.
Susan 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. She received ₹1860 as annual interest. However, had she interchanged the amount of investments in the two schemes, she would recieved ₹20 more as annual interest. How much money did she invest in each scheme? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Susan 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. She received ₹1860 as annual interest. However, had she interchanged the amount of investments in the two schemes, she would recieved ₹20 more as annual interest. How much money did she invest in each scheme? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Susan 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. She received ₹1860 as annual interest. However, had she interchanged the amount of investments in the two schemes, she would recieved ₹20 more as annual interest. How much money did she invest in each scheme?.
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Susan 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. She received ₹1860 as annual interest. However, had she interchanged the amount of investments in the two schemes, she would recieved ₹20 more as annual interest. How much money did she invest in each scheme?, a detailed solution for Susan 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. She received ₹1860 as annual interest. However, had she interchanged the amount of investments in the two schemes, she would recieved ₹20 more as annual interest. How much money did she invest in each scheme? has been provided alongside types of Susan 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. She received ₹1860 as annual interest. However, had she interchanged the amount of investments in the two schemes, she would recieved ₹20 more as annual interest. How much money did she invest in each scheme? theory, EduRev gives you an
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