Question : Directions: Which two signs and two numbers should be interchanged to make the following equation correct?
840 ÷ 38 – 7 + 10 × 12 = 462

Option 1: 12 and 10, ÷ and +

Option 2: 12 and 38, × and –

Option 3: 12 and 7, + and ×

Option 4: 840 and 10, + and –

Correct Answer: 12 and 38, × and –

Solution : Given:
840 ÷ 38 – 7 + 10 × 12 = 462

Let's check the options –
First option: 12 and 10, ÷ and +
On interchanging the numbers and signs, the equation becomes –
840 + 38 – 7 ÷ 12 × 10 = 462
Solving the L.H.S. of the equation –
=  840 + 38 – 0.583 × 10
= 840 + 38 – 5.83
= 872.17 ≠ 462
Second option: 12 and 38, × and –
On interchanging the numbers and signs, the equation becomes –
840 ÷ 12 × 7 + 10 – 38 = 462
Solving the L.H.S. of the equation –
= 70 × 7 + 10 – 38
= 490 + 10 – 38
= 500 – 38
= 462
Third option: 12 and 7, + and ×
On interchanging the numbers and signs, the equation becomes –
840 ÷ 38 – 12 × 10 + 7 = 462
Solving the L.H.S. of the equation –
= 22.10 – 12 × 10 + 7
= 22.10 – 120 + 7
= –90.9 ≠ 462
Fourth option: 840 and 10, + and –
On interchanging the numbers and signs, the equation becomes –
10 ÷ 38 + 7 – 840 × 12 = 462
Solving the L.H.S. of the equation –
= 0.263 + 7 – 840 × 12
= 0.263 + 7 – 10080
= –10072.737 ≠ 462

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