Each question has four options(A), (B), (C) and (D) for answers. Select the right answer and write in English letters in the box against each question in the enclosed answer sheet.
A General, while arranging his men, who were 6000 in number, in the form of a square, found that there were 71 men left over. How many were arranged in each row?

Options

A. 73
B. 77
C. 87
D. 93

Answer

To solve the problem step by step, we need to find out how many men were arranged in each row when a general has 6000 men and 71 men were left over after arranging them in a square formation.

### Step 1: Calculate the number of men that were arranged
First, we need to find out how many men were actually arranged in the square formation. This can be calculated by subtracting the number of men left over from the total number of men.

\[ \text{Number of men arranged} = \text{Total men} - \text{Men left over} \]

\[ \text{Number of men arranged} = 6000 - 71 = 5929 \]

### Step 2: Set up the equation for a square formation
In a square formation, the number of rows is equal to the number of columns. If we denote the number of rows (and columns) as \( x \), then the total number of men arranged can be expressed as:

\[ x^2 = 5929 \]

### Step 3: Solve for \( x \)
To find \( x \), we need to take the square root of both sides of the equation:

\[ x = \sqrt{5929} \]

### Step 4: Calculate the square root
Now we will calculate the square root of 5929.

Using the long division method or a calculator, we find:

\[ \sqrt{5929} = 77 \]

### Step 5: Conclusion
Thus, the number of men arranged in each row is:

\[ \text{Number of men in each row} = 77 \]

The correct answer is (B) 77.

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