Math Problem Statement

PASSAGE Please read the question carefully and select the best choice to fill in the blank. 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 If the average amount invested by all the given persons is Rs. 63000 and the amount invested by B is Rs. 10000 more than the amount invested by D, then the amount invested by B. OPTIONS L PERSONS PRINCIPLE NUMBER OF YEARS(N) RATE OF INTEREST (RN) SIMPLE INTEREST A 75000

12%

B

28800

90000 4 10% 36000 D

8%

E 40000 2

Rs. 45000 Rs. 50000 Rs. 60000. R5. 65000

Solution

To solve the problem, we need to find the amount invested by B, given the following information:

  1. The average amount invested by all five persons is Rs. 63,000.
  2. The amount invested by B is Rs. 10,000 more than the amount invested by D.

Step 1: Set up variables for missing values

Let:

  • PBP_B be the amount invested by B (which we need to find).
  • PDP_D be the amount invested by D.

From the second condition in the question, we know: PB=PD+10,000P_B = P_D + 10,000

Step 2: Use the average condition

The total amount invested by all five persons is the sum of their investments. Given the average investment is Rs. 63,000, the total amount invested by all five persons is: Total investment=63,000×5=315,000\text{Total investment} = 63,000 \times 5 = 315,000 We are also given:

  • PA=75,000P_A = 75,000
  • PE=40,000P_E = 40,000 Thus, the total investment from A, D, and E (with D's value still unknown) is: PA+PD+PE=75,000+PD+40,000=115,000+PDP_A + P_D + P_E = 75,000 + P_D + 40,000 = 115,000 + P_D

Step 3: Set up the equation for the total

Now, the total amount invested by all five persons (A, B, C, D, and E) must be equal to Rs. 315,000. So: PA+PB+PC+PD+PE=315,000P_A + P_B + P_C + P_D + P_E = 315,000 Substitute the known values: 75,000+PB+90,000+PD+40,000=315,00075,000 + P_B + 90,000 + P_D + 40,000 = 315,000 Simplify: 205,000+PB+PD=315,000205,000 + P_B + P_D = 315,000 Since PB=PD+10,000P_B = P_D + 10,000, substitute this into the equation: 205,000+(PD+10,000)+PD=315,000205,000 + (P_D + 10,000) + P_D = 315,000 Simplify further: 205,000+2PD+10,000=315,000205,000 + 2P_D + 10,000 = 315,000 2PD+215,000=315,0002P_D + 215,000 = 315,000 2PD=100,0002P_D = 100,000 PD=50,000P_D = 50,000

Step 4: Calculate PBP_B

Now that we know PD=50,000P_D = 50,000, use the relation PB=PD+10,000P_B = P_D + 10,000: PB=50,000+10,000=60,000P_B = 50,000 + 10,000 = 60,000

Final Answer:

The amount invested by B is Rs. 60,000.

The correct option is Rs. 60,000.


Would you like further clarification on any step? Here are 5 related questions for practice:

  1. What is the formula for calculating simple interest?
  2. How do you calculate the average of a group of numbers?
  3. If B invested Rs. 60,000 at 10% for 4 years, what is the simple interest earned?
  4. What would happen to the average investment if D had invested Rs. 60,000 instead?
  5. How does increasing the investment by Rs. 10,000 affect the total interest earned?

Tip: Always start by summarizing known information and setting up equations before solving complex word problems.

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Math Problem Analysis

Mathematical Concepts

Simple Interest
Investment Calculation
Average Calculation

Formulas

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Theorems

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Suitable Grade Level

Grades 9-10