Which two digits and signs can be interchanged so as to balance the given equation?

328 - 82 + 120 X 6 ÷ 41 = 646

Solution

Given Equation: 328 - 82 + 120 X 6 ÷ 41 = 646 Interchanging the digits and signs given in option 'a', we get: 328 ÷ 6 + 120 X 82 - 41 = 646 LHS = 328 ÷ 6 + 120 X 82 - 41 Cannot be determined as '328' is not completely divisible by '6'. Interchanging the digits and signs given in option 'b', we get: 328 ÷ 41 + 120 X 6 - 82 = 646 LHS = 8 + 120 X 6 - 82 = 8 + 720 - 82 = 728 - 82 = 646 646 = 646 LHS = RHS Interchanging the digits and signs given in option 'c', we get: 328 - 41 + 120 ÷ 6 X 82 = 646 LHS = 328 - 41 + 120 ÷ 6 X 82 = 328 - 41 + 20 X 82 = 328 - 41 + 1640 = 1968 - 41 = 1927 1927 ≠ 646 LHS ≠ RHS Interchanging the digits and signs given in option 'd', we get: 328 - 82 ÷ 6 X 120 + 41 = 646 LHS = 328 - 82 ÷ 6 X 120 + 41 = 328 - 1640 + 41 = 369 - 1640 = -1271 -1271 ≠ 646 LHS ≠ RHS So, only after interchanging the digits and signs given in option 'b', we can get a balanced equation. Hence, option b.