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The simple interest on a certain sum of money at 4% per annum for 5 years is 100 more than the interest on the same sum for 3 years at 5% per annum. Find the sum
- a)1000
- b)1500
- c)2000
- d)2500
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The simple interest on a certain sum of money at 4% per annum for 5 ye...
Answer – c) 2000 Explanation : p*(4/100)*5 – p*(5/100)*3 = 100
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The simple interest on a certain sum of money at 4% per annum for 5 ye...
To solve this problem, let's break it down into smaller steps:
Step 1: Understand the problem
We are given two scenarios:
1. The interest on a certain sum of money at 4% per annum for 5 years.
2. The interest on the same sum for 3 years at 5% per annum.
The problem states that the interest in the first scenario is 100 more than the interest in the second scenario.
Step 2: Set up the equations
Let's assume the principal sum of money is 'P'.
According to the first scenario:
Simple Interest = P * (4/100) * 5 = 0.20P
According to the second scenario:
Simple Interest = P * (5/100) * 3 = 0.15P
Step 3: Solve the equations
The problem states that the interest in the first scenario is 100 more than the interest in the second scenario. Therefore, we can set up the equation:
0.20P = 0.15P + 100
Simplifying the equation, we have:
0.05P = 100
Dividing both sides of the equation by 0.05, we get:
P = 2000
Step 4: Find the sum of money
We have found that the principal sum of money is 2000. Therefore, the answer is option C - 2000.
To summarize:
- Principal sum of money = 2000
- The interest on the sum at 4% per annum for 5 years = 100 more than the interest on the sum at 5% per annum for 3 years.
Step 1: Understand the problem
We are given two scenarios:
1. The interest on a certain sum of money at 4% per annum for 5 years.
2. The interest on the same sum for 3 years at 5% per annum.
The problem states that the interest in the first scenario is 100 more than the interest in the second scenario.
Step 2: Set up the equations
Let's assume the principal sum of money is 'P'.
According to the first scenario:
Simple Interest = P * (4/100) * 5 = 0.20P
According to the second scenario:
Simple Interest = P * (5/100) * 3 = 0.15P
Step 3: Solve the equations
The problem states that the interest in the first scenario is 100 more than the interest in the second scenario. Therefore, we can set up the equation:
0.20P = 0.15P + 100
Simplifying the equation, we have:
0.05P = 100
Dividing both sides of the equation by 0.05, we get:
P = 2000
Step 4: Find the sum of money
We have found that the principal sum of money is 2000. Therefore, the answer is option C - 2000.
To summarize:
- Principal sum of money = 2000
- The interest on the sum at 4% per annum for 5 years = 100 more than the interest on the sum at 5% per annum for 3 years.
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The simple interest on a certain sum of money at 4% per annum for 5 years is 100 more than the interest on the same sum for 3 years at 5% per annum. Find the suma)1000b)1500c)2000d)2500e)None of theseCorrect answer is option 'C'. Can you explain this answer?
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