If ‘+’ means ‘−’, ‘−’ means ‘×’, ‘×’ means ‘÷’, ‘÷’ means ‘+’, then what will…

Concept

In symbol-substitution (interchange-of-operators) reasoning questions, every mathematical symbol stated in the expression must first be replaced by the meaning assigned to it in the question. Only after this substitution is complete should the resulting expression be evaluated, following the standard order of operations (BODMAS): multiplication and division are carried out before addition and subtraction, and operations of equal precedence are carried out from left to right.

Application

1. The given expression is 123 + 7 − 108 × 9 ÷ 16, with the substitution rule ‘+’ → ‘−’, ‘−’ → ‘×’, ‘×’ → ‘÷’, ‘÷’ → ‘+’.

2. Replacing every symbol with its assigned meaning converts the expression into 123 − 7 × 108 ÷ 9 + 16.

3. By BODMAS, multiplication and division are evaluated first, left to right: 7 × 108 = 756, and 756 ÷ 9 = 84.

4. The expression now reduces to 123 − 84 + 16.

5. Evaluating left to right, since addition and subtraction share the same precedence: 123 − 84 = 39, and 39 + 16 = 55.

Cross-check

Since multiplication and division carry equal precedence, dividing before multiplying should give the same intermediate value: 108 ÷ 9 = 12, and 7 × 12 = 84 — identical to the value obtained above, confirming the middle term. Substituting this back, 123 − 84 + 16 = 55 either way.

Hence, the value that replaces the question mark is 55.