Question : Directions: By interchanging the given two signs and numbers which of the following equations will be correct?
+ and –, 2 and 4

Option 1: 9 – 5 ÷ 4 × 2 + 8 = 80

Option 2: 7 × 4 – 2 ÷ 1 + 5 = 13

Option 3: 7 – 8 ÷ 2 + 16 × 4 = 18 

Option 4: 5 + 7 × 4 – 8 ÷ 2 = 5

Correct Answer: 7 × 4 – 2 ÷ 1 + 5 = 13

Solution : Let's check the options –
First option: 9 – 5 ÷ 4 × 2 + 8 = 80
On interchanging the given signs and numbers, the equation becomes –
⇒ 9 + 5 ÷ 2 × 4 – 8 = 80
Solving the L.H.S. of the equation –
= 9 + 5 ÷ 2 × 4 – 8
= 9 + 10 – 8
= 19 – 8
= 11 ≠ 80
Second option: 7 × 4 – 2 ÷ 1 + 5 = 13
On interchanging the given signs and numbers, the equation becomes –
⇒ 7 × 2 + 4 ÷ 1 – 5 = 13
Solving the L.H.S. of the equation –
= 7 × 2 + 4 ÷ 1 – 5
= 7 × 2 + 4 – 5
= 14 + 4 – 5
= 13
Third option: 7 – 8 ÷ 2 + 16 × 4 = 18
On interchanging the given signs and numbers, the equation becomes –
⇒ 7 + 8 ÷ 4 – 16 × 2 = 18
Solving the L.H.S. of the equation –
= 7 + 8 ÷ 4 – 16 × 2
= 7 + 2 – 16 × 2
= 7 + 2 – 32
= –23 ≠ 18
Fourth option: 5 + 7 × 4 – 8 ÷ 2 = 5
On interchanging the given signs and numbers, the equation becomes –
⇒ 5 – 7 × 2 + 8 ÷ 4 = 5
Solving the L.H.S. of the equation –
= 5 – 7 × 2 + 8 ÷ 4
= 5 – 7 × 2 + 2
= 5 – 14 + 2
= –7 ≠ 5

So, only the equation in the second option satisfies the R.H.S. of the given equation. Hence, the second option is correct.