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

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:
- \( P_B \) be the amount invested by B (which we need to find).
- \( P_D \) be the amount invested by D.

From the second condition in the question, we know:
\[ P_B = P_D + 10,000 \]

### 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:
\[
\text{Total investment} = 63,000 \times 5 = 315,000
\]
We are also given:
- \( P_A = 75,000 \)
- \( P_E = 40,000 \)
Thus, the total investment from A, D, and E (with D's value still unknown) is:
\[
P_A + P_D + P_E = 75,000 + P_D + 40,000 = 115,000 + P_D
\]

### 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:
\[
P_A + P_B + P_C + P_D + P_E = 315,000
\]
Substitute the known values:
\[
75,000 + P_B + 90,000 + P_D + 40,000 = 315,000
\]
Simplify:
\[
205,000 + P_B + P_D = 315,000
\]
Since \( P_B = P_D + 10,000 \), substitute this into the equation:
\[
205,000 + (P_D + 10,000) + P_D = 315,000
\]
Simplify further:
\[
205,000 + 2P_D + 10,000 = 315,000
\]
\[
2P_D + 215,000 = 315,000
\]
\[
2P_D = 100,000
\]
\[
P_D = 50,000
\]

### Step 4: Calculate \( P_B \)
Now that we know \( P_D = 50,000 \), use the relation \( P_B = P_D + 10,000 \):
\[
P_B = 50,000 + 10,000 = 60,000
\]

### 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.

Learn how to calculate investment amounts using principal, interest rates, and simple interest in this math problem. Understand how to find missing values such as the amount invested by B based on given conditions. Suitable for students in Grades 9-10.

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