Question : Directions: Which two numbers and two signs can be interchanged to balance the given equation?
16 × 4 + 12 ÷ 4 – 15 = 59

Option 1: 4 and 12; × and ÷

Option 2: 12 and 15; ÷ and –

Option 3: 16 and 12; + and –

Option 4: 15 and 16; × and +

Correct Answer: 16 and 12; + and –

Solution : Given:
16 × 4 + 12 ÷ 4 – 15 = 59

Let's check each option –
First option: 4 and 12; × and ÷
Since there are two 4s in the given equation, it is not clear which 4 should be interchanged with 12. Therefore, this option is incorrect.
Second option: 12 and 15; ÷ and –
On interchanging the mathematical signs and numbers, we get –
16 × 4 + 15 – 4 ÷ 12 = 59
On solving the L.H.S. of the equation –
= 16 × 4 + 15 – 4 ÷ 12
= 16 × 4 + 15 – 0.33
= 64 + 15 – 0.33
= 78.67 ≠ 59
Third option: 16 and 12; + and –
On interchanging the mathematical signs and numbers, we get –
12 × 4 – 16 ÷ 4 + 15 = 59
On solving the L.H.S. of the equation –
= 12 × 4 – 16 ÷ 4 + 15
= 12 × 4 – 4 + 15
= 48 – 4 + 15
= 59
Fourth option: 15 and 16; × and +
On interchanging the mathematical signs and numbers, we get –
15 + 4 × 12 ÷ 4 – 16 = 59
On solving the L.H.S. of the equation –
= 15 + 4 × 12 ÷ 4 – 16
= 15 + 4 × 3 – 16
= 15 + 12 – 16
= 11 ≠ 59

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