Colonel, Major and General started a work together fort ₹ 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. ₹ 256
B. ₹ 144
C. ₹ 85
D. can’t be determined

Answer

To solve the problem, we need to determine the amount of work done by each person (Colonel, Major, and General) and then find out who is the least efficient among them based on the amount of money they receive.

### Step 1: Define the total work
Let's assume the total work is represented by \( W = 17 \) (as suggested in the video transcript).

### Step 2: Calculate the work done by Colonel and Major
According to the problem, Colonel and Major together did \( \frac{8}{17} \) of the total work. Therefore, the work done by Colonel and Major is:
\[ \text{Work by Colonel and Major} = \frac{8}{17} \times 17 = 8 \]

### Step 3: Calculate the work done by Major and General
The problem states that Major and General together did \( \frac{12}{17} \) of the total work. Thus, the work done by Major and General is:
\[ \text{Work by Major and General} = \frac{12}{17} \times 17 = 12 \]

### Step 4: Set up equations for individual work
Let:
- \( C \) = work done by Colonel
- \( M \) = work done by Major
- \( G \) = work done by General

From the above calculations, we can set up the following equations:
1. \( C + M = 8 \) (Equation 1)
2. \( M + G = 12 \) (Equation 2)

### Step 5: Solve the equations
From Equation 1, we can express \( C \) in terms of \( M \):
\[ C = 8 - M \]

Substituting \( C \) in Equation 2:
\[ M + G = 12 \implies G = 12 - M \]

### Step 6: Find the total work done
The total work done by Colonel, Major, and General is:
\[ C + M + G = 17 \]
Substituting the values of \( C \) and \( G \):
\[ (8 - M) + M + (12 - M) = 17 \]
This simplifies to:
\[ 8 + 12 - M = 17 \implies 20 - M = 17 \implies M = 3 \]

### Step 7: Calculate work done by Colonel and General
Now substituting \( M = 3 \) back into the equations:
1. From Equation 1:
\[ C = 8 - 3 = 5 \]
2. From Equation 2:
\[ G = 12 - 3 = 9 \]

### Step 8: Determine the least efficient person
Now we have:
- Colonel's work \( C = 5 \)
- Major's work \( M = 3 \)
- General's work \( G = 9 \)

The least efficient person is the one who did the least amount of work, which is the Major.

### Step 9: Calculate the amount received by each person
The total payment is ₹816. The payment is distributed in proportion to the work done:
- Total work done = \( C + M + G = 5 + 3 + 9 = 17 \)

Calculating the amount received by each:
- Colonel's share:
\[ \text{Colonel's amount} = \frac{C}{17} \times 816 = \frac{5}{17} \times 816 = 240 \]
- Major's share:
\[ \text{Major's amount} = \frac{M}{17} \times 816 = \frac{3}{17} \times 816 = 144 \]
- General's share:
\[ \text{General's amount} = \frac{G}{17} \times 816 = \frac{9}{17} \times 816 = 432 \]

### Conclusion
The amount received by the least efficient person (Major) is ₹144.

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