Question : Directions: Which two signs should be interchanged in the given equation to make it mathematically correct?
26 ÷ 24 + 6 × 27 − 105 = 29

Option 1: × and ÷

Option 2: + and ÷

Option 3: + and ×

Option 4: × and −

Correct Answer: + and ÷

Solution : Given:
26 ÷ 24 + 6 × 27 − 105 = 29

Let's check each option –
First Option: × and ÷
On interchanging the mathematical signs, we get –
26 × 24 + 6 ÷ 27 − 105 = 29
On solving the L.H.S. of the equation –
= 26 × 24 + 6 ÷ 27 − 105
= 26 × 24 + 0.22 − 105
= 624 + 0.22 − 105
= 519.22 ≠ 29
Second Option: + and ÷
On interchanging the mathematical signs, we get –
26 + 24 ÷ 6 × 27 − 105 = 29
On solving the L.H.S. of the equation –
= 26 + 24 ÷ 6 × 27 − 105
= 26 + 4 × 27 − 105
= 26 + 108 − 105
= 29
Third Option: + and ×
On interchanging the mathematical signs, we get –
26 ÷ 24 × 6 + 27 − 105 = 29
On solving the L.H.S. of the equation –
= 26 ÷ 24 × 6 + 27 − 105
= 6.5 + 27 − 105
= –71.5 ≠ 29
Fourth Option: × and –
On interchanging the mathematical signs, we get –
26 ÷ 24 + 6 – 27 × 105 = 29
On solving the L.H.S. of the equation –
= 26 ÷ 24 + 6 – 27 × 105
= 1.083 + 6 – 27 × 105
= 1.083 + 6 – 2835
= –2827.917 ≠ 29

So, only the second option satisfies the equation. Hence, the second option is correct.