Question : Directions: Which two signs and two numbers should be interchanged in the following equation to make it correct?
19 + 27 – 4 ÷ 2 × 3 = 20

Option 1: – and ÷; 4 and 3

Option 2: ÷ and ×; 19 and 27

Option 3: – and +; 27 and 2

Option 4: + and ×; 3 and 2

Correct Answer: – and ÷; 4 and 3

Solution : Given:
19 + 27 – 4 ÷ 2 × 3 = 20

Let's check each option –
First Option: – and ÷; 4 and 3
On interchanging the mathematical signs and numbers, we get –
19 + 27 ÷ 3 – 2 × 4 = 20
On solving the L.H.S. of the equation –
= 19 + 27 ÷ 3 – 2 × 4
= 19 + 9 – 2 × 4
= 19 + 9 – 8
= 28 – 8
= 20
Second Option: ÷ and ×; 19 and 27
On interchanging the mathematical signs and numbers, we get –
27 + 19 – 4 × 2 ÷ 3 = 20
On solving the L.H.S. of the equation –
= 27 + 19 – 4 × 2 ÷ 3
= 27 + 19 – 4 × 0.67
= 27 + 19 – 2.68
= 43.32 ≠ 20
Third Option: – and +; 27 and 2
On interchanging the mathematical signs and numbers, we get –
19 – 2 + 4 ÷ 27 × 3 = 20
On solving the L.H.S. of the equation –
= 19 – 2 + 4 ÷ 27 × 3
= 19 – 2 + 0.148 × 3
= 19 – 2 + 0.444
= 17.444 ≠ 20
Fourth Option: + and ×; 3 and 2
On interchanging the mathematical signs and numbers, we get –
19 × 27 – 4 ÷ 3 + 2 = 20
On solving the L.H.S. of the equation –
= 19 × 27 – 4 ÷ 3 + 2
= 19 × 27 – 1.33 + 2
= 513 – 1.33 + 2
= 513.67 ≠ 20

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