Question : Directions: Which two numbers, from amongst the given options, should be interchanged to make the given equation correct?
72 + (7 × 8) – (126 ÷ 14) – (4)² = 150

Option 1: 72 and 126

Option 2: 7 and 4

Option 3: 8 and 4

Option 4: 14 and 7

Correct Answer: 14 and 7

Solution : Given:
72 + (7 × 8) – (126 ÷ 14) – (4) ² = 150

Let's check the options –
First option: 72 and 126
On interchanging the numbers, we get –
⇒ 126 + (7 × 8) – (72 ÷ 14) – (4) ² = 150
Solving the L.H.S. of the equation –
= 126 + (7 × 8) – (72 ÷ 14) – (4) ²
= 126 + 56 – 5.14 – 16
= 182 – 5.14 – 16
= 160.86 ≠ 150
Second option: 7 and 4
On interchanging the numbers, we get –
⇒ 72 + (4 × 8) – (126 ÷ 14) – (7) ² = 150
Solving the L.H.S. of the equation –
= 72 + (4 × 8) – (126 ÷ 14) – (7) ²
= 72 + 32 – 9 – 49
= 104 – 9 – 49
= 46 ≠ 150
Third option: 8 and 4
On interchanging the numbers, we get –
⇒ 72 + (7 × 4) – (126 ÷ 14) – (8) ² = 150
Solving the L.H.S. of the equation –
= 72 + (7 × 4) – (126 ÷ 14) – (8) ²
= 72 + 28 – 9 – 64
= 100 – 9 – 64
= 27 ≠ 150
Fourth option: 14 and 7
On interchanging the numbers, we get –
⇒ 72 + (14 × 8) – (126 ÷ 7) – (4) ² = 150
Solving the L.H.S. of the equation –
= 72 + (14 × 8) – (126 ÷ 7) – (4) ²
= 72 + 112 – 18 – 16
= 184 – 18 – 16
= 150

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