In a class test, the sum of Kamal's marks in mathematics and English is 40. Had he got 3 marks more in mathematics and 4 marks less in English, the product of the marks would have been 360. Find his marks in two subjects separately.

Explanation

To solve the problem, let's denote Kamal's marks in Mathematics as \( x \) and his marks in English as \( y \).

### Step 1: Set up the equations
From the problem, we know two things:

1. The sum of Kamal's marks in Mathematics and English is 40:
\[ x + y = 40 \]

2. If he got 3 marks more in Mathematics and 4 marks less in English, the product of the marks would have been 360:
\[ (x + 3)(y - 4) = 360 \]

### Step 2: Substitute \( y \)
From the first equation, we can express \( y \) in terms of \( x \):
\[ y = 40 - x \]

### Step 3: Substitute \( y \) into the second equation
Now, substitute \( y \) into the second equation:
\[ (x + 3)((40 - x) - 4) = 360 \]
This simplifies to:
\[ (x + 3)(36 - x) = 360 \]

### Step 4: Expand the equation
Now, expand the left side:
\[ x \cdot 36 - x^2 + 3 \cdot 36 - 3x = 360 \]
This simplifies to:
\[ 36x - x^2 + 108 - 3x = 360 \]
Combining like terms gives:
\[ - x^2 + 33x + 108 = 360 \]

### Step 5: Rearrange the equation
Rearranging the equation gives:
\[ - x^2 + 33x + 108 - 360 = 0 \]
This simplifies to:
\[ -x^2 + 33x - 252 = 0 \]
Multiplying through by -1 gives:
\[ x^2 - 33x + 252 = 0 \]

### Step 6: Factor the quadratic equation
Next, we need to factor the quadratic equation:
\[ x^2 - 33x + 252 = 0 \]
We look for two numbers that multiply to 252 and add to -33. The factors are -21 and -12:
\[ (x - 21)(x - 12) = 0 \]

### Step 7: Solve for \( x \)
Setting each factor to zero gives us:
\[ x - 21 = 0 \quad \text{or} \quad x - 12 = 0 \]
Thus, we find:
\[ x = 21 \quad \text{or} \quad x = 12 \]

### Step 8: Find corresponding \( y \) values
Now we can find the corresponding \( y \) values using \( y = 40 - x \):
1. If \( x = 21 \):
\[ y = 40 - 21 = 19 \]
2. If \( x = 12 \):
\[ y = 40 - 12 = 28 \]

### Conclusion
Kamal's marks in Mathematics and English can be:
- \( (21, 19) \) or \( (12, 28) \)