Which two signs should be interchanged to make the below equation mathematically correct?

48×4+5÷3 2=25

Appeared in: DSSSB - 28 August 2019 (Shift-1)

Explanation

The core principle for solving this is the BODMAS rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction), which dictates the sequence of operations.
By interchanging the multiplication (×) and division (÷) signs, the equation becomes 48 ÷ 4 + 5 × 3 - 2.
Following BODMAS, we first perform division: 48 ÷ 4 = 12.
Next, we perform multiplication: 5 × 3 = 15.
Finally, we perform addition and subtraction from left to right: 12 + 15 - 2 = 27 - 2 = 25.
This result matches the right-hand side of the equation, confirming the interchange is correct.

Option A: Interchanging '+' and '÷' gives the equation 48 × 4 ÷ 5 + 3 - 2. Following BODMAS, this evaluates to (192 ÷ 5) + 3 - 2 = 38.4 + 1 = 39.4, which is not equal to 25.
Option C: Interchanging '×' and '+' gives the equation 48 + 4 × 5 ÷ 3 - 2. Following BODMAS, this evaluates to 48 + (20 ÷ 3) - 2 ≈ 48 + 6.67 - 2 = 52.67, which is not equal to 25.
Option D: Interchanging '+' and '-' gives the equation 48 × 4 - 5 ÷ 3 + 2. Following BODMAS, this evaluates to 192 - (5 ÷ 3) + 2 ≈ 192 - 1.67 + 2 = 192.33, which is not equal to 25.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Mathematical Reasoning: Operator Interchange as background academic context rather than a clinical decision trigger.
While not a clinical question, this type of logical reasoning and attention to detail is crucial for nurses.
Nurses use similar step-by-step, rule-based thinking for tasks like calculating drug dosages, where the order of operations is critical to prevent errors.
This skill ensures accuracy in high-stakes situations, preventing medication errors and ensuring patient safety.

How to Approach the Question

First, read the question carefully to understand the task: you need to swap two mathematical signs to make the equation correct.
Recall the BODMAS/PEMDAS rule for the order of operations. This is the key to solving the problem.
Take the first option and mentally (or on paper) swap the signs in the original equation.
Calculate the value of the left-hand side of the new equation using the BODMAS rule.
Check if the calculated value equals the right-hand side (25 in this case).
If it doesn't match, move to the next option and repeat the process until you find the correct pair of signs.

Concept Tested & Keywords

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Practise the full DSSSB - 28 August 2019 (Shift-1)

Attempt every question from this paper in a timed mock, then review the full solution for each one.