A and B together complete 11/19 part of the work. In the same time B and C together com plete 14/19 part of the work. Accordingly find the ratio of work done by A, B, and C?

Options

A. ` 3:4:5 `
B. `4:5:7`
C. `5:6:8 `
D. `5:7:8`

Answer

To solve the problem, we need to determine the ratio of work done by A, B, and C based on the information provided. Let's break it down step by step.

### Step 1: Understand the information given
A and B together complete \( \frac{11}{19} \) of the work, and B and C together complete \( \frac{14}{19} \) of the work.

### Step 2: Determine the total work
Since A, B, and C are working together, we can assume the total work is represented as 19 units (this is a convenient choice since the fractions given have a denominator of 19).

### Step 3: Calculate work done by C
From the first piece of information:
- A + B = \( \frac{11}{19} \) of the work
- Therefore, the work done by C can be calculated as:
\[ C = 19 - (A + B) = 19 - 11 = 8 \text{ units} \]

### Step 4: Calculate work done by A
From the second piece of information:
- B + C = \( \frac{14}{19} \) of the work
- Therefore, the work done by A can be calculated as:
\[ A = 19 - (B + C) = 19 - 14 = 5 \text{ units} \]

### Step 5: Calculate work done by B
Now that we have the work done by A and C, we can find the work done by B:
- We know that:
\[ A + B + C = 19 \]
- Substituting the values we have:
\[ 5 + B + 8 = 19 \]
- Simplifying this gives:
\[ B = 19 - 13 = 6 \text{ units} \]

### Step 6: Write the ratio of work done by A, B, and C
Now we have:
- Work done by A = 5 units
- Work done by B = 6 units
- Work done by C = 8 units

The ratio of work done by A, B, and C is:
\[ A : B : C = 5 : 6 : 8 \]

### Final Answer
Thus, the ratio of work done by A, B, and C is \( 5 : 6 : 8 \).

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