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A certain sum of money becomes three times of itself in 20 years at simple interest. In how many years will the initial sum become double at the same rate of simple interest?
- a)8
- b)10
- c)12
- d)14
Correct answer is option 'B'. Can you explain this answer?
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A certain sum of money becomes three times of itself in 20 years at si...
Let Principal = x Amount = 3x Simple interest = 2x
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A certain sum of money becomes three times of itself in 20 years at si...
Let's assume the initial sum of money is P.
According to the question, this sum becomes three times itself in 20 years at simple interest. This means that after 20 years, the amount will be 3P.
We can use the formula for simple interest to calculate the amount after 20 years:
A = P + P * r * t
where A is the final amount, P is the principal (initial sum of money), r is the rate of interest, and t is the time in years.
In this case, we know that after 20 years, the final amount is 3P. So we can write:
3P = P + P * r * 20
Simplifying the equation, we get:
3 = 1 + 20r
Now, we need to find out in how many years the initial sum will become double at the same rate of simple interest. Let's assume this time to be 'n' years.
Using the same formula for simple interest, we can write:
2P = P + P * r * n
Simplifying the equation, we get:
2 = 1 + nr
To find the value of 'n', we can equate the two equations we derived:
1 + 20r = 1 + nr
Simplifying the equation, we get:
20r = nr
Dividing both sides of the equation by r, we get:
20 = n
Therefore, the initial sum will become double at the same rate of simple interest in 20 years.
According to the question, this sum becomes three times itself in 20 years at simple interest. This means that after 20 years, the amount will be 3P.
We can use the formula for simple interest to calculate the amount after 20 years:
A = P + P * r * t
where A is the final amount, P is the principal (initial sum of money), r is the rate of interest, and t is the time in years.
In this case, we know that after 20 years, the final amount is 3P. So we can write:
3P = P + P * r * 20
Simplifying the equation, we get:
3 = 1 + 20r
Now, we need to find out in how many years the initial sum will become double at the same rate of simple interest. Let's assume this time to be 'n' years.
Using the same formula for simple interest, we can write:
2P = P + P * r * n
Simplifying the equation, we get:
2 = 1 + nr
To find the value of 'n', we can equate the two equations we derived:
1 + 20r = 1 + nr
Simplifying the equation, we get:
20r = nr
Dividing both sides of the equation by r, we get:
20 = n
Therefore, the initial sum will become double at the same rate of simple interest in 20 years.
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A certain sum of money becomes three times of itself in 20 years at simple interest. In how many years will the initial sum become double at the same rate of simple interest?a)8b)10c)12d)14Correct answer is option 'B'. Can you explain this answer?
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