Colonel, Major and General started a work together for Rs. 816. Colonel and Major did `(8)/(17)` of the total work, while Major and General together did `(12)/(17)`of the whole work. What is the amount of the least efficient person?

Options

A. Rs. 256
B. Rs. 144
C. Rs. 85
D. can't be determined.

Answer

To solve the problem, we need to find the amount earned by the least efficient person among Colonel, Major, and General based on the work they did together.

### Step 1: Understand the Work Distribution
We know that:
- Colonel and Major together did \( \frac{8}{17} \) of the total work.
- Major and General together did \( \frac{12}{17} \) of the total work.

Let the total work be represented as 17 units (for simplicity).

### Step 2: Calculate Work Done by Colonel and Major
If the total work is 17 units, then the work done by Colonel and Major together is:
\[ C + M = \frac{8}{17} \times 17 = 8 \text{ units} \]

### Step 3: Calculate Work Done by Major and General
Similarly, the work done by Major and General together is:
\[ M + G = \frac{12}{17} \times 17 = 12 \text{ units} \]

### Step 4: Set Up the Equations
Now we have two equations:
1. \( C + M = 8 \) (Equation 1)
2. \( M + G = 12 \) (Equation 2)

### Step 5: Solve for General's Work
From Equation 1, we can express Colonel's work in terms of Major's work:
\[ C = 8 - M \quad \text{(Equation 3)} \]

Substituting Equation 3 into Equation 2:
\[ M + G = 12 \implies G = 12 - M \quad \text{(Equation 4)} \]

### Step 6: Find Work Done by Each Person
Now we have:
- Colonel's work: \( C = 8 - M \)
- Major's work: \( M \)
- General's work: \( G = 12 - M \)

### Step 7: Find the Value of M
To find the individual work done by each person, we can add the total work done:
\[ C + M + G = 17 \]
Substituting the values from Equations 3 and 4:
\[ (8 - M) + M + (12 - M) = 17 \]
Simplifying:
\[ 8 + 12 - M = 17 \implies 20 - M = 17 \implies M = 3 \]

### Step 8: Calculate Work Done by Colonel and General
Now substituting \( M = 3 \) back into Equations 3 and 4:
- Colonel's work:
\[ C = 8 - 3 = 5 \]
- General's work:
\[ G = 12 - 3 = 9 \]

### Step 9: Identify the Least Efficient Person
The work done by each person is:
- Colonel: 5 units
- Major: 3 units
- General: 9 units

The least efficient person is Major, who did 3 units of work.

### Step 10: Calculate the Amount Earned by the Least Efficient Person
The total payment for the work is Rs. 816. The amount earned by each unit of work is:
\[ \text{Amount per unit} = \frac{816}{17} = 48 \]

Thus, the amount earned by Major (least efficient person) is:
\[ \text{Amount for Major} = 3 \text{ units} \times 48 = 144 \]

### Final Answer
The amount earned by the least efficient person (Major) is Rs. 144.

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