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
- Find the simple interest (in ₹) on ₹4,000 at 6.75% per annum rate of interest deposited on 21 February 2024 and withdrawn on 22 April 2024.
- Sapna invested ₹21,900 on simple interest, partly at 14% per annum and partly at 10% per annum. If she earns equal interests from the two investments after 2 years, then find the sum invested at 14% per annum (in ₹).
- A sum of ₹800 becomes ₹920 in 3 years at simple interest. If interest is increased by 4%, then the amount will increase to:
- An amount becomes eight-fifth of the original amount in 5 years at what percentage rate of simple interest per annum?
- The rate at which a sum becomes 2 times of itself in 10 years at simple interest is:
- Find the simple interest (in ₹) on ₹4,000 at 7.5% per annum rate of interest deposited on 4 February 2024 and withdrawn on 5 April 2024.
- How many years will it take for an amount of ₹400 to yield ₹450 as interest at 5% per annum on simple interest?
- Vikas took a loan of ₹1,200 on simple interest that is equal to as many years as the rate of interest. If he paid ₹768 as interest at the end of the loan period, then what was the rate of interest?
- A sum of money amounts to ₹12,000 after 6 years and ₹15,000 after 9 years at the same rate of simple interest. What is the rate of interest per annum?
- What will be the amount of simple interest on ₹75,000 at the rate of $2\frac{5}{3}\%$ per annum for a period of 5 years?
Important Questions from Simple Interest
How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest ?
Nirav and Mehul borrowed Rs.4000 and Rs.5000 respectively for 2.5 years at the rate of x% per annum. Mehul paid Rs 125 more interest than Nirav. Find x.
If the interest on a sum of Rs.1200 is more than the interest on Rs.1000 by Rs.120 in three years, then what is the rate of interest per annum?.
The difference between the simple interest received from two banks on Rs. 500 for two years is Rs. 2.50. What is the difference between their rates?
A sum of Rs.1200 becomes Rs.1560 at a rate of simple interest in 3 years. In how many years will the sum of Rs.800 amount to Rs.1120 at the same rate of simple interest?
