Simplify the equation 12.5 × 14 ÷ 8.75 + 42 = 50 + ? and find the value that should replace the question mark so that both sides of the equation are equal.

Introduction / Context:
This question tests your ability to handle decimal multiplication and division, and then to rearrange an equation to solve for an unknown. Such expressions often appear in quantitative aptitude questions involving unit conversions and scaled values.

Given Data / Assumptions:

• The equation is 12.5 × 14 ÷ 8.75 + 42 = 50 + ?.
• We need to evaluate the left hand side and then determine the unknown value ? on the right hand side to balance the equation.
• All calculations involve real decimal numbers.

Concept / Approach:
First, use the correct order of operations on the left hand side: perform multiplication and division before addition. Once we find the numerical value of the left hand side, we set it equal to 50 + ? and isolate ? by subtracting 50. Careful handling of decimals ensures an accurate result.

Step-by-Step Solution:
Evaluate the product 12.5 × 14. This equals 175.0 because 12.5 × 10 = 125 and 12.5 × 4 = 50, so total is 175.Now divide 175 by 8.75: 175 ÷ 8.75 = 20 because 8.75 × 20 = 175.Add 42 to this result: 20 + 42 = 62.So the left hand side simplifies to 62, giving the equation 62 = 50 + ?.Subtract 50 from both sides to isolate ?: ? = 62 − 50 = 12.

Verification / Alternative check:
Substitute ? = 12 back into the original equation. The right hand side becomes 50 + 12 = 62. Since we already simplified the left hand side to 62, both sides are equal, so the equation balances perfectly. The intermediate step 175 ÷ 8.75 = 20 can be checked by noting that both numerator and denominator can be multiplied by 100, giving 17500 ÷ 875, which also equals 20.

Why Other Options Are Wrong:

• 18 or 20 would make the right hand side 68 or 70, which do not match 62.
• 32 and 42 are much larger, leading to right hand side totals far from the left hand side.
• Only 12 produces a right hand side exactly equal to the simplified left hand side.

Common Pitfalls:

• Mistakes in multiplying 12.5 by 14 or dividing by 8.75.
• Adding 42 before completing the multiplication and division.
• Incorrectly isolating the unknown by adding instead of subtracting 50 from 62.

Final Answer:
12