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Tarun invested an amount of Rs. 10000 at the simple interest rate of 8% per annum and another amount at the simple interest rate of 20% per annum. The total interest earned at the end of one year on the total amount invested became 12% per annum. Find the total amount invested.
- a)Rs.12,000
- b)Rs.15000
- c)Rs.5,000
- d)Rs.10,000
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Tarun invested an amount of Rs. 10000 at the simple interest rate of 8...
Answer – B.Rs.15000 Explanation : SI1= 10000*8*1/100 = 800
SI2 = x*20*1/100 = x/5 800+(x/5) = (10000+x)*12*1/100 80000+20x = 1,20,000+12x 8x = 40,000 X = 5000
Total= 10000+5000 = 15000
SI2 = x*20*1/100 = x/5 800+(x/5) = (10000+x)*12*1/100 80000+20x = 1,20,000+12x 8x = 40,000 X = 5000
Total= 10000+5000 = 15000
Most Upvoted Answer
Tarun invested an amount of Rs. 10000 at the simple interest rate of 8...
To solve this problem, we can use the formula for simple interest:
Simple Interest = Principal Amount × Rate × Time
Let's assume that Tarun invested an amount of Rs. x at 8% per annum and another amount at 20% per annum.
1. Calculation for the amount invested at 8% per annum:
The simple interest earned on this amount is (x × 8 × 1)/100 = 8x/100
2. Calculation for the amount invested at 20% per annum:
The simple interest earned on this amount is [(10000 - x) × 20 × 1]/100 = (2000 - 20x)/100
3. Total interest earned at the end of one year on the total amount invested:
According to the question, the total interest earned at the end of one year on the total amount invested is 12% per annum. So, the simple interest earned on the total amount is (10000 × 12 × 1)/100 = 1200
4. Equating the total interest earned to the sum of the interest earned on each amount:
8x/100 + (2000 - 20x)/100 = 1200
Simplifying the equation:
8x + 2000 - 20x = 120000
-12x = -118000
x = 118000/12
x = 9833.33
5. Finding the total amount invested:
The total amount invested is the sum of the amounts invested at 8% and 20% per annum:
Total amount invested = x + (10000 - x) = 9833.33 + (10000 - 9833.33) = 9833.33 + 166.67 = 10000
Therefore, the total amount invested is Rs. 10000 (option d).
Simple Interest = Principal Amount × Rate × Time
Let's assume that Tarun invested an amount of Rs. x at 8% per annum and another amount at 20% per annum.
1. Calculation for the amount invested at 8% per annum:
The simple interest earned on this amount is (x × 8 × 1)/100 = 8x/100
2. Calculation for the amount invested at 20% per annum:
The simple interest earned on this amount is [(10000 - x) × 20 × 1]/100 = (2000 - 20x)/100
3. Total interest earned at the end of one year on the total amount invested:
According to the question, the total interest earned at the end of one year on the total amount invested is 12% per annum. So, the simple interest earned on the total amount is (10000 × 12 × 1)/100 = 1200
4. Equating the total interest earned to the sum of the interest earned on each amount:
8x/100 + (2000 - 20x)/100 = 1200
Simplifying the equation:
8x + 2000 - 20x = 120000
-12x = -118000
x = 118000/12
x = 9833.33
5. Finding the total amount invested:
The total amount invested is the sum of the amounts invested at 8% and 20% per annum:
Total amount invested = x + (10000 - x) = 9833.33 + (10000 - 9833.33) = 9833.33 + 166.67 = 10000
Therefore, the total amount invested is Rs. 10000 (option d).
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Tarun invested an amount of Rs. 10000 at the simple interest rate of 8% per annum and another amount at the simple interest rate of 20% per annum. The total interest earned at the end of one year on the total amount invested became 12% per annum. Find the total amount invested.a)Rs.12,000b)Rs.15000c)Rs.5,000d)Rs.10,000e)None of theseCorrect answer is option 'B'. Can you explain this answer?
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