Evaluate the numerical expression 69 ÷ 3 × 0.85 + 24.5 − 13.8 using the correct BODMAS order of operations and determine the final result.

Introduction / Context:
This question tests basic numerical calculation skills using the correct order of operations, often remembered by the rule BODMAS or PEMDAS. The task is to carefully apply division and multiplication before addition and subtraction, while working with decimals accurately, which is important in many aptitude and banking examinations.

Given Data / Assumptions:

• The expression to evaluate is 69 ÷ 3 × 0.85 + 24.5 − 13.8.
• Operations must follow the standard order: division and multiplication from left to right, then addition and subtraction.
• All numbers are real decimal values.

Concept / Approach:
According to BODMAS, we first perform any division and multiplication operations in the expression, proceeding from left to right. After that, we handle addition and subtraction in order from left to right. Keeping track of decimal places and performing each step accurately prevents rounding errors and incorrect intermediate results.

Step-by-Step Solution:
Start with the expression: 69 ÷ 3 × 0.85 + 24.5 − 13.8.First perform the division: 69 ÷ 3 = 23.Next, multiply the result by 0.85: 23 × 0.85 = 19.55.Add 24.5 to this result: 19.55 + 24.5 = 44.05.Finally, subtract 13.8: 44.05 − 13.8 = 30.25.

Verification / Alternative check:
We can double check the calculation by using approximate mental arithmetic. 69 ÷ 3 is exactly 23. Multiplying 23 by 0.85 is the same as taking 85 percent of 23. Since 10 percent of 23 is 2.3, 80 percent is 18.4 and 5 percent is 1.15, so 18.4 + 1.15 = 19.55, which matches the earlier result. Adding 24.5 gives about 44.05, and subtracting 13.8 brings us to 30.25. The consistency of both detailed and approximate calculations confirms that 30.25 is correct.

Why Other Options Are Wrong:

• 31.75 and 28.95 likely result from performing operations in the wrong order or misplacing decimal points.
• 35.25 may come from an incorrect addition step before the subtraction.
• 32.15 is a close but incorrect approximation that suggests a rounding or arithmetic slip.

Common Pitfalls:

• Performing addition or subtraction before completing all division and multiplication operations.
• Incorrectly handling multiplication by a decimal such as 0.85.
• Dropping or misplacing decimal digits at intermediate steps.

Final Answer:
30.25