Math Problem Statement
Study the following table charts carefully and answer the questions given beside. the following table shows the principal amount invested by five different person ins a scheme and the number of years and the rate of interest they are provided for the investment and the simple interest they earned after a certain period also given. Some values are missing
Please read the question carefully and select the best choice to fill in the blank.
If the simple interest earned by C is Rs. 4000 less than the simple interest earn by A.
Then find the number of year. A invested the amount.
OPTIONS
PERSONS
PRINCIPLE
NUMBER
OF
YEARS(N)
RATE OF
INTEREST (R79)
SIMPLE
INTEREST
A
75000
12%
3
28800
90000
4
10%
36000
D
6
8%
E
40000
2
4.4 Years
5.6 Years
6 years
8.5 years
Solution
To solve the problem, we need to find the number of years that A invested his amount, given that the simple interest (SI) earned by C is Rs. 4,000 less than the simple interest earned by A.
Step 1: Recall the formula for simple interest
The formula for calculating simple interest is: where:
- is the principal amount,
- is the rate of interest per annum, and
- is the number of years.
Step 2: Known values for person A
From the table, we are given:
- Principal invested by A:
- Rate of interest for A:
- Simple interest earned by A: (unknown, but we will calculate it).
The simple interest for A is given by the formula: Substitute the known values: Thus, the simple interest for A is:
Step 3: Known values for person C
For person C, we are given:
- Principal invested by C:
- Number of years for C:
- Rate of interest for C:
- Simple interest earned by C: (from the table).
The simple interest for C can be calculated using the same formula:
Step 4: Use the relation between and
We are given that the simple interest earned by C is Rs. 4,000 less than the simple interest earned by A. So, we can write: Substitute into the equation:
Step 5: Solve for
Now, we know that , and from Step 2, we have: Equating the two expressions for : Solve for :
Step 6: Compare with the given options
The closest option to years is 4.4 years.
Final Answer:
The number of years A invested the amount is 4.4 years.
Would you like further clarifications on any steps? Here are 5 related questions for practice:
- How would the result change if A had invested Rs. 80,000 instead of Rs. 75,000?
- What would be the simple interest earned by A if he had invested for 6 years at 12%?
- How does changing the rate of interest affect the simple interest earned over time?
- What is the total interest earned by all five persons together?
- If C had invested for 5 years instead of 4, what would his new simple interest be?
Tip: For word problems, start by organizing known values and equations clearly to simplify your calculations.
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Math Problem Analysis
Mathematical Concepts
Simple Interest
Percentage
Equations
Formulas
Simple Interest formula: SI = (P * R * N) / 100
Theorems
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Suitable Grade Level
Grades 9-12