Question : Directions: Which two signs and two numbers should be interchanged in the following equation to make it correct?
60 × 3 + 660 ÷ 6 – 20 = 290

Option 1: 6 and 660; × and ÷

Option 2: 20 and 6; + and –

Option 3: 20 and 60; + and ×

Option 4: 20 and 660; + and ÷

Correct Answer: 20 and 60; + and ×

Solution : Given:
60 × 3 + 660 ÷ 6 – 20 = 290

Let's check the given options –
First option: 6 and 660; × and ÷
On interchanging, the mathematical signs and numbers, we get –
60 ÷ 3 + 6 × 660 – 20 = 290
Solving the L.H.S. of the given equation –
= 60 ÷ 3 + 6 × 660 – 20
= 20 + 6 × 660 – 20
= 20 + 3960 – 20
= 3980 – 20
= 3960 ≠ 290
Second option: 20 and 6, + and –
On interchanging, the mathematical signs and numbers, we get –
60 × 3 – 660 ÷ 20 + 6 = 290
Solving the L.H.S. of the given equation –
= 60 × 3 – 660 ÷ 20 + 6
= 60 × 3 – 33 + 6
= 180 – 33 + 6
= 186 – 33
= 153 ≠ 290
Third option: 20 and 60, + and ×
On interchanging, the mathematical signs and numbers, we get –
20 + 3 × 660 ÷ 6 – 60 = 290
Solving the L.H.S. of the given equation –
= 20 + 3 × 660 ÷ 6 – 60
= 20 + 3 × 110 – 60
= 20 + 330 – 60
= 350 – 60
= 290 = R.H.S.
Fourth option: 20 and 660, + and ÷
On interchanging, the mathematical signs and numbers, we get –
60 × 3 ÷ 20 + 6 – 660 = 290
Solving the L.H.S. of the given equation –
= 60 × 3 ÷ 20 + 6 – 660
= 9 + 6 – 660
= 14 – 660
= – 646 ≠ 290

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