This problem involves calculating time based on simple interest principles. We need to find how long it takes for an initial sum of money to become three times its original value.
Calculating Simple Interest Timeframe
Let the principal sum be P.
- Scenario 1: Sum Doubles
- Amount becomes 2P.
- Simple Interest (SI) = Amount - Principal = 2P - P = P.
- Time (T1) = 4 years 4 months. Convert this to years: $ T_1 = 4 + \frac{4}{12} \text{ years} = 4 + \frac{1}{3} \text{ years} = \frac{12+1}{3} \text{ years} = \frac{13}{3} \text{ years} $
- Scenario 2: Sum Triples
- Amount becomes 3P.
- Simple Interest (SI) = Amount - Principal = 3P - P = 2P.
- Time (T2) = ? (This is what we need to find).
Simple Interest Relationship
For simple interest, the interest earned is directly proportional to the time period, provided the principal and rate remain constant. We can write this relationship as:
$ \frac{SI_1}{T_1} = \frac{SI_2}{T_2} $Substitute the values from our two scenarios:
$ \frac{P}{\frac{13}{3}} = \frac{2P}{T_2} $Finding the Tripling Time
Now, solve for T2. First, cancel P from both sides:
$ \frac{1}{\frac{13}{3}} = \frac{2}{T_2} $Simplify the left side:
$ \frac{3}{13} = \frac{2}{T_2} $Cross-multiply to find T2:
$ T_2 = 2 \times \frac{13}{3} $ $ T_2 = \frac{26}{3} \text{ years} $Convert the improper fraction to a mixed number:
$ T_2 = 8 \frac{2}{3} \text{ years} $This matches the time required for the sum to triple itself.
Similar Questions
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Important Questions from Simple Interest
Anil lent a sum of Rs. 5,000 on simple interest for 10 years in such a way that the rate of interest is 6% per annum for the first 2 years, 8% per anmum for the next 2 years and 10% per annum beyond 4 years. How much interest (in Rs.) will he earn at the end of 10 years?
What will be the simple interest on a sum of Rs. 12000 at the rate of 15 percent per annum for three years ?
If in 13 years fixed sum doubles at simple interest, what will be the interest rate per year? (correct to two decimal places)
On simple interest a sum of Rs. 640 becomes Rs. 832 in 2 years. What will Rs. 860 become in 4 years at the same rate of simple interest?
A certain sum amounts to Rs. 81840 in 3 years and to Rs. 92400 in 5 years at x% p.a. under simple interest. If the rate of interest is becomes (x + 2)%, then in how many years will the same sum double itself?
