Question : Directions: Which two numbers should be interchanged to make the given equation correct?
84 ÷ 6 + 16 – 14 × 2 = 10
Option 1: 6 and 14
Option 2: 2 and 84
Option 3: 10 and 14
Option 4: 6 and 10
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.
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