Question : Directions: Which of the following interchange of mathematical signs would make the given equation correct?
20 ÷ 4 × 8 + 16 – 15 = 11

Option 1: – and ÷

Option 2: + and –

Option 3: × and ÷

Option 4: + and ×

Correct Answer: × and ÷

Solution : Given:
20 ÷ 4 × 8 + 16 – 15 = 11

Let's check the given options –
First option: – and ÷
On interchanging the mathematical signs, we get –
⇒ 20 – 4 × 8 + 16 ÷ 15 = 11
Solving the L.H.S. of the equation –
= 20 – 4 × 8 + 16 ÷ 15
= 20 – 4 × 8 + 1.067
= 20 – 32 + 1.067
= 21.067 – 32
= –10.933 ≠ 11
Second option: + and –
On interchanging the mathematical signs, we get –
⇒ 20 ÷ 4 × 8 – 16 + 15 = 11
Solving the L.H.S. of the equation –
= 20 ÷ 4 × 8 – 16 + 15
= 5 × 8 – 16 + 15
= 40 – 16 + 15
= 55 – 16
= 39 ≠ 11
Third option: × and ÷
On interchanging the mathematical signs, we get –
⇒ 20 × 4 ÷ 8 + 16 – 15 = 11
Solving the L.H.S. of the equation –
= 20 × 4 ÷ 8 + 16 – 15
= 20 × 0.5 + 16 – 15
= 10 + 16 – 15
= 26 – 15
= 11
Fourth option: + and ×
On interchanging the mathematical signs, we get –
⇒ 20 ÷ 4 + 8 × 16 – 15 = 11
Solving the L.H.S. of the equation –
= 20 ÷ 4 + 8 × 16 – 15
= 5 + 8 × 16 – 15
= 5 + 128 – 15
= 133 – 15
= 118 ≠ 11

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