If a + b means a - b; a - b means a × b; a × b means a ÷ b; a ÷ b means a + b, then what is the value of 10 + 30 - 100 × 50 ÷ 25? (Operations are to be replaced simultaneously)
- (a) 15
- (b) 0
- (c) -15
- (d) -25 ✓ UPSC's answer
Why the answer is (d)
• The problem states that operations are to be replaced simultaneously, which means we must first substitute the symbols in the expression with their defined meanings before applying the standard order of operations (BODMAS/PEMDAS).
• The given expression is 10 + 30 - 100 × 50 ÷ 25. Applying the simultaneous replacement: '+' becomes '-', '-' becomes '×', '×' becomes '÷', and '÷' becomes '+'.
• After substitution, the new expression is 10 - 30 × 100 ÷ 50 + 25.
• Following the order of operations, we first perform the division and multiplication from left to right. The division 100 ÷ 50 equals 2.
• Next, we perform the multiplication: 30 × 2 equals 60. The expression now simplifies to 10 - 60 + 25.
• Finally, we perform the addition and subtraction from left to right: 10 - 60 equals -50, and -50 + 25 equals -25, so the answer is option (d).
Why the other options are wrong
- (a) 15
- This value likely results from an incorrect order of operations or a miscalculation during the substitution phase, failing to account for the simultaneous replacement of symbols.
- (b) 0
- This value would be obtained if the multiplication and division were ignored or if the signs were mishandled, leading to a net zero which is not supported by the arithmetic.
- (c) -15
- This value is incorrect as it does not match the result of applying the standard order of operations to the substituted expression 10 - 30 × 100 ÷ 50 + 25.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2024, held on 16 June 2024. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.