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 NAN_A 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: SI=P×R×N100SI = \frac{P \times R \times N}{100} where:

  • PP is the principal amount,
  • RR is the rate of interest per annum, and
  • NN is the number of years.

Step 2: Known values for person A

From the table, we are given:

  • Principal invested by A: PA=75,000P_A = 75,000
  • Rate of interest for A: RA=12%R_A = 12\%
  • Simple interest earned by A: SIASI_A (unknown, but we will calculate it).

The simple interest for A is given by the formula: SIA=PA×RA×NA100SI_A = \frac{P_A \times R_A \times N_A}{100} Substitute the known values: SIA=75,000×12×NA100=9,000×NASI_A = \frac{75,000 \times 12 \times N_A}{100} = 9,000 \times N_A Thus, the simple interest for A is: SIA=9,000×NASI_A = 9,000 \times N_A

Step 3: Known values for person C

For person C, we are given:

  • Principal invested by C: PC=90,000P_C = 90,000
  • Number of years for C: NC=4N_C = 4
  • Rate of interest for C: RC=10%R_C = 10\%
  • Simple interest earned by C: SIC=36,000SI_C = 36,000 (from the table).

The simple interest for C can be calculated using the same formula: SIC=PC×RC×NC100=90,000×10×4100=36,000SI_C = \frac{P_C \times R_C \times N_C}{100} = \frac{90,000 \times 10 \times 4}{100} = 36,000

Step 4: Use the relation between SIASI_A and SICSI_C

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: SIA=SIC+4,000SI_A = SI_C + 4,000 Substitute SIC=36,000SI_C = 36,000 into the equation: SIA=36,000+4,000=40,000SI_A = 36,000 + 4,000 = 40,000

Step 5: Solve for NAN_A

Now, we know that SIA=40,000SI_A = 40,000, and from Step 2, we have: SIA=9,000×NASI_A = 9,000 \times N_A Equating the two expressions for SIASI_A: 9,000×NA=40,0009,000 \times N_A = 40,000 Solve for NAN_A: NA=40,0009,0004.44 yearsN_A = \frac{40,000}{9,000} \approx 4.44 \text{ years}

Step 6: Compare with the given options

The closest option to NA4.44N_A \approx 4.44 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:

  1. How would the result change if A had invested Rs. 80,000 instead of Rs. 75,000?
  2. What would be the simple interest earned by A if he had invested for 6 years at 12%?
  3. How does changing the rate of interest affect the simple interest earned over time?
  4. What is the total interest earned by all five persons together?
  5. 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