What will come in the place of ‘?’ in the following equation, if ‘÷’ and ‘–‘ are interchanged and ‘×’ and ‘+’ are interchanged?

15 × 9 + 7 ÷ 26 – 13 = ?

Question

What will come in the place of ‘?’ in the following equation, if ‘÷’ and ‘–‘ are interchanged and ‘×’ and ‘+’ are interchanged?

15 × 9 + 7 ÷ 26 – 13 = ?

Accepted Answer

Let's analyze the operator interchanges:
- ‘÷’ and ‘–‘ are interchanged: So wherever there is ‘÷’, use ‘–‘, and wherever there is ‘–‘, use ‘÷’.
- ‘×’ and ‘+’ are interchanged: So wherever there is ‘×’, use ‘+’, and wherever there is ‘+’, use ‘×’.

Original equation:
15 × 9 + 7 ÷ 26 – 13 = ?

Now, replace the operators:
- 15 × 9 → 15 + 9
- + becomes ×, so 9 + 7 becomes 9 × 7
- 7 ÷ 26: ÷ becomes –, so 7 – 26
- – becomes ÷, so 26 – 13 becomes 26 ÷ 13

But let's clarify the structure. The original equation is:
15 × 9 + 7 ÷ 26 – 13

Let's rewrite with brackets for clarity:
(15 × 9) + (7 ÷ 26) – 13

Now, substitute the operators:
- × → +
- + → ×
- ÷ → –
- – → ÷

So,
(15 × 9) + (7 ÷ 26) – 13
becomes
(15 + 9) × (7 – 26) ÷ 13

Now, let's solve step by step:
1. 15 + 9 = 24
2. 7 – 26 = -19
3. So, (15 + 9) × (7 – 26) = 24 × (-19) = -456
4. Now, divide by 13: -456 ÷ 13 = -35.0769

Wait, but the operator precedence is:
(15 + 9) × (7 – 26) ÷ 13
First, multiply, then divide.
So,
24 × (-19) = -456
-456 ÷ 13 = -35.0769

But none of the options are negative or decimal. Let's check if the operator mapping is correct.

Alternatively, perhaps the mapping is:
- × and + are interchanged: × → +, + → ×
- ÷ and – are interchanged: ÷ → –, – → ÷

So, the equation:
15 × 9 + 7 ÷ 26 – 13
Becomes:
15 + 9 × 7 – 26 ÷ 13
But that's not matching the mapping.

Let's try mapping each operator in order:
- 15 × 9: × → +, so 15 + 9
- + 7: + → ×, so × 7
- ÷ 26: ÷ → –, so – 26
- – 13: – → ÷, so ÷ 13

So, the equation becomes:
(15 + 9) × 7 – 26 ÷ 13
But this is ambiguous. Let's write with brackets:
((15 + 9) × 7) – (26 ÷ 13)

Now, let's solve step by step:
1. 15 + 9 = 24
2. 24 × 7 = 168
3. 26 ÷ 13 = 2
4. 168 – 2 = 166

But 166 is not among the options.

Alternatively, perhaps the mapping is:
- 15 × 9: × → +, so 15 + 9 = 24
- + 7: + → ×, so 24 × 7 = 168
- ÷ 26: ÷ → –, so 168 – 26 = 142
- – 13: – → ÷, so 142 ÷ 13 = 10.923

Again, not matching the options.

Alternatively, perhaps the mapping is:
- 15 × 9: × → +, so 15 + 9 = 24
- + 7: + → ×, so 24 × 7 = 168
- ÷ 26: ÷ → –, so 168 – 26 = 142
- – 13: – → ÷, so 142 ÷ 13 = 10.923

Still not matching.

Alternatively, perhaps the equation is:
15 × 9 + 7 ÷ 26 – 13
So, after mapping:
15 + 9 × 7 – 26 ÷ 13
Now, apply BODMAS:
First, multiplication and division:
- 9 × 7 = 63
- 26 ÷ 13 = 2
So, equation becomes:
15 + 63 – 2
Now, addition and subtraction:
15 + 63 = 78
78 – 2 = 76

Now, 76 is one of the options.

Therefore, the correct answer is 76.

Final Answer: 76

Answer

Answer

Answer