A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days, after that B and C left the work. If they got Rs 7500 for that work then how much A get more than C?

Let's solve the problem step by step.

### Step 1: Define the rates of work
Let:
- A's rate of work = \( A \) (work per day)
- B's rate of work = \( B \)
- C's rate of work = \( C \)

From the given information, we can write the following equations:
- A and B together can complete the work in 30 days, so:
  \[
  A + B = \frac{1}{30} \quad \text{(This means A and B together can complete \( \frac{1}{30} \) of the work in 1 day.)}
  \]
- B and C together can complete the work in 24 days, so:
  \[
  B + C = \frac{1}{24}
  \]
- C and A together can complete the work in 20 days, so:
  \[
  C + A = \frac{1}{20}
  \]

### Step 2: Find individual work rates
We have three equations:
1. \( A + B = \frac{1}{30} \)
2. \( B + C = \frac{1}{24} \)
3. \( C + A = \frac{1}{20} \)

To find \( A \), \( B \), and \( C \), let's add all three equations:
\[
(A + B) + (B + C) + (C + A) = \frac{1}{30} + \frac{1}{24} + \frac{1}{20}
\]
This simplifies to:
\[
2(A + B + C) = \frac{1}{30} + \frac{1}{24} + \frac{1}{20}
\]

Now, find the common denominator of 30, 24, and 20. The least common denominator (LCD) is 120, so:
\[
\frac{1}{30} = \frac{4}{120}, \quad \frac{1}{24} = \frac{5}{120}, \quad \frac{1}{20} = \frac{6}{120}
\]
Thus,
\[
2(A + B + C) = \frac{4 + 5 + 6}{120} = \frac{15}{120} = \frac{1}{8}
\]
Dividing both sides by 2:
\[
A + B + C = \frac{1}{16}
\]

### Step 3: Solve for individual rates
Now, use the value \( A + B + C = \frac{1}{16} \) in the original equations to find each person's rate:

1. \( A + B = \frac{1}{30} \)
2. \( B + C = \frac{1}{24} \)
3. \( C + A = \frac{1}{20} \)

From \( A + B + C = \frac{1}{16} \), we know:
\[
A = (A + B + C) - (B + C) = \frac{1}{16} - \frac{1}{24} = \frac{3}{48} - \frac{2}{48} = \frac{1}{48}
\]
So, \( A = \frac{1}{48} \) (A completes \( \frac{1}{48} \) of the work in 1 day).

Now, use this to find \( B \) and \( C \):
- From \( A + B = \frac{1}{30} \), we get:
  \[
  B = \frac{1}{30} - \frac{1}{48} = \frac{8 - 5}{240} = \frac{3}{240} = \frac{1}{80}
  \]
- From \( C + A = \frac{1}{20} \), we get:
  \[
  C = \frac{1}{20} - \frac{1}{48} = \frac{12 - 5}{240} = \frac{7}{240} = \frac{7}{240}
  \]

Thus, \( A = \frac{1}{48}, B = \frac{1}{80}, C = \frac{1}{80} \).



A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days, after that B and C left the work. If they got Rs 7500 for that work, how much does A get more than C?

Solve a complex work and time problem involving A, B, and C's combined work rates. This step-by-step solution covers core concepts like algebra and rates of work, using key formulas for work distribution. Suitable for students in Grades 9-12.

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