Question : Directions: Which two signs need to be interchanged to make the following equation correct?
2 + 78 ÷ 13 – 4 × 111 = 119

Option 1: + and ÷

Option 2: ÷ and ×

Option 3: + and –

Option 4: + and ×

Correct Answer: + and ×

Solution : Given:
2 + 78 ÷ 13 – 4 × 111 = 119

Let's check each option –
First Option: + and ÷
On interchanging the mathematical signs, we get –
2 ÷ 78 + 13 – 4 × 111 = 119
On solving the L.H.S. of the equation –
= 2 ÷ 78 + 13 – 4 × 111
= 0.026 + 13 – 4 × 111
= 0.026 + 13 – 444
= –430.974 ≠ 119
Second Option: ÷ and ×
On interchanging the mathematical signs, we get –
2 + 78 × 13 – 4 ÷ 111 = 119
On solving the L.H.S. of the equation –
= 2 + 78 × 13 – 4 ÷ 111
= 2 + 78 × 13 – 0.036
= 2 + 1014 – 0.036
= 1015.964 ≠ 119
Third Option: + and –
On interchanging the mathematical signs, we get –
2 – 78 ÷ 13 + 4 × 111 = 119
On solving the L.H.S. of the equation –
= 2 – 78 ÷ 13 + 4 × 111
= 2 – 78 ÷ 13 + 4 × 111
= 2 – 6 + 444
= 440 ≠ 119
Fourth Option: + and ×
On interchanging the mathematical signs, we get –
2 × 78 ÷ 13 – 4 + 111 = 119
On solving the L.H.S. of the equation –
= 2 × 78 ÷ 13 – 4 + 111
= 2 × 6 – 4 + 111
= 12 – 4 + 111
= 119

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