Solve for the unknown ? in the percentage equation 41% of 600 − 250 = ? − 77% of 900.

Introduction / Context:
This question checks understanding of percentage calculations and simple linear equations. The expression involves computing percentages of given numbers, then forming and solving an equation to find an unknown value represented by ?. Problems like this are common in arithmetic sections of aptitude exams and in everyday financial reasoning.

Given Data / Assumptions:

• Equation: 41% of 600 − 250 = ? − 77% of 900.

• All percentages are simple fractions of the given base numbers.

• We must find the value of ? that balances the equation.

Concept / Approach:
First we compute 41% of 600 and 77% of 900 by converting percentages to decimals or fractions. After simplifying the left hand side, we express the right hand side in terms of ? and the computed percentage. Equating both sides and solving for ? yields a simple addition. Finally, we choose the matching option from the list provided.

Step-by-Step Solution:
Step 1: Compute 41% of 600. Since 41% = 41/100, we have (41/100) × 600 = 41 × 6 = 246. Step 2: Evaluate the left side: 41% of 600 − 250 = 246 − 250 = −4. Step 3: Compute 77% of 900. Since 77% = 77/100, we have (77/100) × 900 = 77 × 9 = 693. Step 4: Substitute into the right side: ? − 77% of 900 = ? − 693. Step 5: Set the equation: −4 = ? − 693. Step 6: Add 693 to both sides: −4 + 693 = ?, so ? = 689.

Verification / Alternative check:
Verify by substituting ? = 689 back into the original equation. The right side becomes 689 − 77% of 900 = 689 − 693 = −4. The left side was already found to be −4. Since both sides are equal, the value ? = 689 satisfies the equation exactly. No other value will balance the equation because this is a simple one variable linear equation.

Why Other Options Are Wrong:
If ? were 589, the right side would be 589 − 693 = −104, not −4. For ? = 789, the right side becomes 789 − 693 = 96. For ? = 889, we get 889 − 693 = 196. For ? = 609, we get 609 − 693 = −84. None of these match the left side value −4. Only 689 produces equality between left and right sides.

Common Pitfalls:
Common mistakes include miscalculating the percentages, for example computing 41% of 600 as 2460, or mixing up subtraction signs when forming the equation. Some students also move terms across the equals sign without changing their sign correctly. Writing each step clearly and checking intermediate values helps to avoid these errors, especially when time pressure is high in exam conditions.

Final Answer:
The value of the unknown ? that satisfies the equation is 689.