Question : Directions: Which two signs and two numbers should be interchanged in the following equation to make it correct?
14 × 8 + 64 ÷ 32 – 2 = 88

Option 1: 8 and 32; × and +

Option 2: 14 and 2; × and +

Option 3: 8 and 2; – and ÷

Option 4: 32 and 64; + and ÷

Correct Answer: 8 and 2; – and ÷

Solution : Given:
14 × 8 + 64 ÷ 32 – 2 = 88

Let's check each option –
First Option: 8 and 32; × and +
On interchanging the mathematical signs and numbers, we get –
14 + 32 × 64 ÷ 8 – 2 = 88
On solving the L.H.S. of the equation –
= 14 + 32 × 64 ÷ 8 – 2
= 14 + 32 × 8 – 2
= 14 + 256 – 2
= 268 ≠ 88
Second Option: 14 and 2; × and +
On interchanging the mathematical signs and numbers, we get –
2 + 8 × 64 ÷ 32 – 14 = 88
On solving the L.H.S. of the equation –
= 2 + 8 × 64 ÷ 32 – 14
= 2 + 8 × 2 – 14
= 2 + 16 – 14
= 4 ≠ 88
Third Option: 8 and 2; – and ÷
On interchanging the mathematical signs and numbers, we get –
14 × 2 + 64 – 32 ÷ 8 = 88
On solving the L.H.S. of the equation –
= 14 × 2 + 64 – 32 ÷ 8
= 14 × 2 + 64 – 4
= 28 + 64 – 4
= 88
Fourth Option: 32 and 64; + and ÷
On interchanging the mathematical signs and numbers, we get –
14 × 8 ÷ 32 + 64 – 2 = 88
On solving the L.H.S. of the equation –
= 14 × 8 ÷ 32 + 64 – 2
= 14 × 0.25  + 64 – 2
= 3.5 + 64 – 2
= 65.5 ≠ 88

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