Question : Directions: Which two numbers from amongst the given options should be interchanged to make the given equation correct?
248 ÷ 4 + 184 ÷ (4 × 6 – 2 × 8) = 77

Option 1: 8 and 4

Option 2: 184 and 77

Option 3: 184 and 248

Option 4: 4 and 6

Correct Answer: 184 and 248

Solution : Given:
248 ÷ 4 + 184 ÷ (4 × 6 – 2 × 8) = 77

Let's check the options –
First option: 8 and 4
⇒ 248 ÷ 4 + 184 ÷ (4 × 6 – 2 × 8) = 77
Since there are two 4s in the equation, it is unclear which 4 should be interchanged with 8. So, this option is incorrect.
Second option: 184 and 77
⇒ 248 ÷ 4 + 184 ÷ (4 × 6 – 2 × 8) = 77
On interchanging the numbers, the equation becomes –
⇒ 248 ÷ 4 + 77 ÷ (4 × 6 – 2 × 8) = 184
Solving the L.H.S. of the equation –
= 248 ÷ 4 + 77 ÷ (4 × 6 – 2 × 8)
= 248 ÷ 4 + 77 ÷ (24 – 16)
= 248 ÷ 4 + 77 ÷ 8
= 62 + 9.625
= 71.625 ≠ 184
Third option: 184 and 248
⇒ 248 ÷ 4 + 184 ÷ (4 × 6 – 2 × 8) = 77
On interchanging the numbers, the equation becomes –
⇒ 184 ÷ 4 + 248 ÷ (4 × 6 – 2 × 8) = 77
Solving the L.H.S. of the equation –
= 184 ÷ 4 + 248 ÷ (4 × 6 – 2 × 8)
= 184 ÷ 4 + 248 ÷ (24 – 16)
= 184 ÷ 4 + 248 ÷ 8
= 46 + 31
= 77
Fourth option: 4 and 6
⇒ 248 ÷ 4 + 184 ÷ (4 × 6 – 2 × 8) = 77
Since there are two 4s in the equation, it is unclear which 4 should be interchanged with 6. So, this option is incorrect.

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