Question : Directions: Which two signs and two numbers should be interchanged in the following equation to make it correct?
23 × 13 – 195 ÷ 17 + 40 = 366

Option 1: 23 and 40; × and –

Option 2: 23 and 17; × and ÷

Option 3: 13 and 17; × and +

Option 4: 13 and 17; + and –

Correct Answer: 13 and 17; + and –

Solution : Given:
23 × 13 – 195 ÷ 17 + 40 = 366

Let's check each option –
First Option: 23 and 40; × and –
On interchanging the mathematical signs and numbers, we get –
40 – 13 × 195 ÷ 17 + 23 = 366
On solving the L.H.S. of the equation –
= 40 – 13 × 195 ÷ 17 + 23
= 40 – 13 × 11.47 + 23
= 40 – 149.11 + 23
= –86.11 ≠ 366
Second Option: 23 and 17; × and ÷
On interchanging the mathematical signs and numbers, we get –
17 ÷ 13 – 195 × 23 + 40 = 366
On solving the L.H.S. of the equation –
= 17 ÷ 13 – 195 × 23 + 40
= 1.31 – 195 × 23 + 40
= 1.31 – 4485 + 40
= –4443.69 ≠ 366
Third Option: 13 and 17; × and +
On interchanging the mathematical signs and numbers, we get –
23 + 17 – 195 ÷ 13 × 40 = 366
On solving the L.H.S. of the equation –
= 23 + 17 – 195 ÷ 13 × 40
= 23 + 17 – 15 × 40
= 23 + 17 – 600
= –560 ≠ 366
Fourth Option: 13 and 17; + and -
On interchanging the mathematical signs and numbers, we get –
23 × 17 + 195 ÷ 13 – 40 = 366
On solving the L.H.S. of the equation –
= 23 × 17 + 195 ÷ 13 – 40
= 23 × 17 + 15 – 40
= 391 + 15 – 40
= 366

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