In this aptitude (simplification) question, you must find the value that replaces the question mark to keep the numerical equation balanced. Compute 115 / 5 + 12 * 6 on the left side and ? + 64 / 4 - 35 on the right side, using correct order of operations, and determine the missing number ?.

Introduction / Context:
This is a straightforward arithmetic simplification question from the simplification topic in aptitude. Candidates need to apply the correct order of operations, sometimes remembered as BODMAS or PEMDAS, to evaluate both sides of an equation. The aim is to find the number that should replace the question mark so that the equality holds exactly.

Given Data / Assumptions:
We are given the equation 115 / 5 + 12 * 6 = ? + 64 / 4 - 35.
All operations are standard arithmetic in real numbers.
We must find the value of the unknown represented by ?.

Concept / Approach:
The key concept is the order of operations. Multiplication and division are performed before addition and subtraction. We first simplify each arithmetic block step by step, working separately on the left side and on the right side. Once we obtain a numeric value on one side, we can solve the resulting linear equation in the unknown ? by simple addition or subtraction.

Step-by-Step Solution:
Compute the left side: 115 / 5 + 12 * 6. 115 / 5 = 23, and 12 * 6 = 72, so the left side is 23 + 72 = 95. Now simplify the right side: ? + 64 / 4 - 35. 64 / 4 = 16, so the right side is ? + 16 - 35. Combine constants: 16 - 35 = -19, so the right side becomes ? - 19. Set the two sides equal: 95 = ? - 19. Add 19 to both sides: ? = 95 + 19 = 114.

Verification / Alternative check:
Substitute ? = 114 back into the original expression to verify. The right side becomes 114 + 64 / 4 - 35. We already know 64 / 4 = 16, so this is 114 + 16 - 35 = 130 - 35 = 95. This matches the left side, which we computed as 95. Since both sides are equal, the solution ? = 114 is confirmed as correct.

Why Other Options Are Wrong:
If we try 95, the right side would be 95 + 16 - 35 = 76, which is not equal to 95. Option 102 gives 102 + 16 - 35 = 83. Option 136 gives 136 + 16 - 35 = 117. Option 74 gives 74 + 16 - 35 = 55. None of these values makes the right side equal to the left side, so they are all incorrect.

Common Pitfalls:
A common mistake is to perform addition or subtraction before division or multiplication, which changes the result. Another error is incorrect handling of negative numbers when combining constants, for example miscomputing 16 - 35. Carefully following the order of operations and writing intermediate results helps prevent such issues.

Final Answer:
The equation balances only when the missing number is 114.