Question : Directions: By interchanging the given two signs and numbers, which of the following equations will be correct?
+ and ×, 1 and 2

Option 1: 8 × 3 – 4 ÷ 2 + 1 = 7

Option 2: 2 × 3 – 8 ÷ 1 + 9 = 18

Option 3: 8 × 3 – 4 ÷ 2 + 1 = 3

Option 4: 2 × 3 – 8 ÷ 1 + 2 = 5

Correct Answer: 8 × 3 – 4 ÷ 2 + 1 = 3

Solution : Let's check the options –
First option: 8 × 3 – 4 ÷ 2 + 1 = 7
On interchanging the mathematical signs and numbers, we get –
⇒ 8 + 3 – 4 ÷ 1 × 2 = 7
Solving the L.H.S. of the equation –
= 8 + 3 – 4 ÷ 1 × 2
= 8 + 3 – 4 × 2
= 8 + 3 – 8
= 11 – 8
= 3 ≠ 7
Second option: 2 × 3 – 8 ÷ 1 + 9 = 18
On interchanging the mathematical signs and numbers, we get –
⇒ 1 + 3 – 8 ÷ 2 × 9 = 18
Solving the L.H.S. of the equation –
= 1 + 3 – 8 ÷ 2 × 9
= 1 + 3 – 4 × 9
= 1 + 3 – 36
= 4 – 36
= –32 ≠ 18
Third option: 8 × 3 – 4 ÷ 2 + 1 = 3
On interchanging the mathematical signs and numbers, we get –
⇒ 8 + 3 – 4 ÷ 1 × 2 = 3
Solving the L.H.S. of the equation –
= 8 + 3 – 4 ÷ 1 × 2
= 8 + 3 – 4 × 2
= 8 + 3 – 8
= 11 – 8
= 3
Fourth option: 2 × 3 – 8 ÷ 1 + 2 = 5
On interchanging the mathematical signs and numbers, we get –
⇒ 1 + 3 – 8 ÷ 2 × 1 = 5
Solving the L.H.S. of the equation –
= 1 + 3 – 8 ÷ 2 × 1
= 1 + 3 – 4 × 1
= 1 + 3 – 4
= 4 – 4
= 0 ≠ 5

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