Question : Directions: Which two signs and two numbers should be interchanged in the following equation to make it correct?
14 × 6 ÷ 12 + 15 – 9 = 203

Option 1: 15 and 6, + and ÷

Option 2: 12 and 15, – and ×

Option 3: 12 and 9, ÷ and –

Option 4: 14 and 6, ÷ and ×

Correct Answer: 15 and 6, + and ÷

Solution : Given:
14 × 6 ÷ 12 + 15 – 9 = 203

Interchange the signs and numbers given in the equation with the assigned signs and numbers in the options one by one –
First option: 15 and 6, + and ÷
On interchanging the signs and numbers, we get –
⇒ 14 × 15 + 12 ÷ 6 – 9 = 203
Solving the L.H.S. of the equation –
= 14 × 15 + 12 ÷ 6 – 9
= 14 × 15 + 2 – 9
= 210 + 2 – 9
= 212 – 9
= 203
Second option: 12 and 15, – and ×
On interchanging the signs and numbers, we get –
⇒ 14 – 6 ÷ 15 + 12 × 9 = 203
Solving the L.H.S. of the equation –
= 14 – 6 ÷ 15 + 12 × 9
= 14 – 0.4 + 12 × 9
= 14 – 0.4 + 108
= 122 – 0.4
= 121.6 ≠ 203
Third option: 12 and 9, ÷ and –
On interchanging the signs and numbers, we get –
⇒ 14 × 6 – 9 + 15 ÷ 12 = 203
Solving the L.H.S. of the equation –
= 14 × 6 – 9 + 15 ÷ 12
= 14 × 6 – 9 + 1.25
= 84 – 9 + 1.25
= 85.25 – 9
= 76.25 ≠ 203
Fourth option: 14 and 6, ÷ and ×
On interchanging the signs and numbers, we get –
⇒ 6 ÷ 14 × 12 + 15 – 9 = 203
Solving the L.H.S. of the equation –
= 6 ÷ 14 × 12 + 15 – 9
= 0.43 × 12 + 15 – 9
= 5.16 + 15 – 9
= 20.16 – 9
= 11.16 ≠ 203

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