Correct Answer: 6 and 14

Solution : Given:
84 ÷ 6 + 16 – 14 × 2 = 10

Let's check the given options –
First option: 6 and 14
On interchanging the numbers, we get –
84 ÷ 14 + 16 – 6 × 2 = 10
Solving the L.H.S. of the given equation –
= 84 ÷ 14 + 16 – 6 × 2
= 6 + 16 – 6 × 2
= 6 + 16 – 12
= 10
Second option: 2 and 84
On interchanging the numbers, we get –
2 ÷ 6 + 16 – 14 × 84 = 10
Solving the L.H.S. of the given equation –
= 2 ÷ 6 + 16 – 14 × 84
= 0.33 + 16 – 14 × 84
= 0.33 + 16 – 1176
= –1159.67 ≠ 10
Third option: 10 and 14
On interchanging the numbers, we get –
84 ÷ 6 + 16 – 10 × 2 = 14
Solving the L.H.S. of the given equation –
= 84 ÷ 6 + 16 – 10 × 2
= 14 + 16 – 10 × 2
= 14 + 16 – 20
= 10 ≠ 14
Fourth option: 6 and 10
On interchanging the numbers, we get –
84 ÷ 10 + 16 – 14 × 2 = 6
Solving the L.H.S. of the given equation –
= 84 ÷ 10 + 16 – 14 × 2
= 8.4 + 16 – 14 × 2
= 8.4 + 16 – 28
= –3.6 ≠ 6

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