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A certain sum of money is invested for one year at a certain rate of simple interest. If the rate of interest is 3% higher, then the interest earned will be 25% more than the interest earned earlier. What is the earlier rate of interest ?
- a)4% p.a.
- b)6% p.a.
- c)8% p.a.
- d)12% p.a.
Correct answer is option 'D'. Can you explain this answer?
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A certain sum of money is invested for one year at a certain rate of s...
Let 
be the rate of interest:
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be the rate of interest: r = 12% per annum
Most Upvoted Answer
A certain sum of money is invested for one year at a certain rate of s...
To solve this problem, let's assume the initial rate of interest is 'x' percent.
Given that the rate of interest is increased by 3%, the new rate of interest will be (x + 3) percent.
According to the problem, the interest earned at the new rate is 25% more than the interest earned earlier.
Let's denote the initial sum of money invested as 'P'.
1. Calculate the initial interest earned:
The formula for calculating simple interest is:
Interest = (Principal * Rate * Time) / 100
So, the interest earned at the initial rate of interest 'x' is:
Interest1 = (P * x * 1) / 100 = Px/100
2. Calculate the interest earned at the increased rate:
The interest earned at the increased rate of interest (x + 3) is:
Interest2 = (P * (x + 3) * 1) / 100 = P(x + 3)/100
3. According to the problem, the interest earned at the increased rate is 25% more than the interest earned earlier.
Mathematically, this can be expressed as:
Interest2 = Interest1 + (25/100) * Interest1
Substituting the values of Interest1 and Interest2, we get:
P(x + 3)/100 = Px/100 + (25/100) * Px/100
Simplifying the equation further:
P(x + 3) = Px + (25/100) * Px
Px + 3P = Px + (25/100) * Px
3P = (25/100) * Px
3P = (1/4) * Px
Canceling out Px from both sides of the equation:
3 = 1/4
This equation is not possible. Hence, our assumption that the initial rate of interest is 'x' percent is incorrect.
Therefore, the initial rate of interest must be 12% p.a. (Option D) for the equation to hold true.
Given that the rate of interest is increased by 3%, the new rate of interest will be (x + 3) percent.
According to the problem, the interest earned at the new rate is 25% more than the interest earned earlier.
Let's denote the initial sum of money invested as 'P'.
1. Calculate the initial interest earned:
The formula for calculating simple interest is:
Interest = (Principal * Rate * Time) / 100
So, the interest earned at the initial rate of interest 'x' is:
Interest1 = (P * x * 1) / 100 = Px/100
2. Calculate the interest earned at the increased rate:
The interest earned at the increased rate of interest (x + 3) is:
Interest2 = (P * (x + 3) * 1) / 100 = P(x + 3)/100
3. According to the problem, the interest earned at the increased rate is 25% more than the interest earned earlier.
Mathematically, this can be expressed as:
Interest2 = Interest1 + (25/100) * Interest1
Substituting the values of Interest1 and Interest2, we get:
P(x + 3)/100 = Px/100 + (25/100) * Px/100
Simplifying the equation further:
P(x + 3) = Px + (25/100) * Px
Px + 3P = Px + (25/100) * Px
3P = (25/100) * Px
3P = (1/4) * Px
Canceling out Px from both sides of the equation:
3 = 1/4
This equation is not possible. Hence, our assumption that the initial rate of interest is 'x' percent is incorrect.
Therefore, the initial rate of interest must be 12% p.a. (Option D) for the equation to hold true.
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A certain sum of money is invested for one year at a certain rate of simple interest. If the rate of interest is 3% higher, then the interest earned will be 25% more than the interest earned earlier. What is the earlier rate of interest ?a)4% p.a.b)6% p.a.c)8% p.a.d)12% p.a.Correct answer is option 'D'. Can you explain this answer?
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