Question : Directions: By interchanging the given two signs and numbers which of the following equations will not be correct?
÷ and ×, 1 and 3

Option 1: 6 ÷ 3 – 1 + 4 × 2 = 5

Option 2: 4 × 3 – 1 + 8 ÷ 2 = 9

Option 3: 5 – 8 × 3 + 9 ÷ 1 = 24

Option 4: 6 + 4 – 9 × 3 ÷ 1 = –17

Correct Answer: 4 × 3 – 1 + 8 ÷ 2 = 9

Solution : Given:
÷ and ×, 1 and 3

Let's check the options –
First option: 6 ÷ 3 – 1 + 4 × 2 = 5
On replacing the numbers and mathematical signs, the equation becomes –
⇒ 6 × 1 – 3 + 4 ÷ 2 = 5
Solving the L.H.S. of the given equation –
= 6 × 1 – 3 + 4 ÷ 2
= 6 × 1 – 3 + 2
= 6 – 3 + 2
= 5
Second option: 4 × 3 – 1 + 8 ÷ 2 = 9
On replacing the numbers and mathematical signs, the equation becomes –
⇒ 4 ÷ 1 – 3 + 8 × 2 = 9
Solving the L.H.S. of the given equation –
= 4 ÷ 1 – 3 + 8 × 2
= 4 – 3 + 16
= 17 ≠ 9
Third option: 5 – 8 × 3 + 9 ÷ 1 = 24
On replacing the numbers and mathematical signs, the equation becomes –
⇒ 5 – 8 ÷ 1 + 9 × 3 = 24
Solving the L.H.S. of the given equation –
= 5 – 8 ÷ 1 + 9 × 3
= 5 – 8 + 9 × 3
= 5 – 8 + 27
= 24
Fourth option: 6 + 4 – 9 × 3 ÷ 1 = –17
On replacing the numbers and mathematical signs, the equation becomes –
⇒ 6 + 4 – 9 ÷ 1 × 3 = –17
Solving the L.H.S. of the given equation –
= 6 + 4 – 9 ÷ 1 × 3
= 6 + 4 – 9 × 3
= 6 + 4 – 27
= –17

So, only the second option does not satisfy the equation after interchanging the signs and numbers. Hence, the second option is correct.