Question : Directions: Which two mathematical signs should be interchanged to make the given equation correct?
(75 + 15) × 27 × 1 – 9 ÷ 7 × (135 + 3) – 10 ÷ (189 + 63) = 434

Option 1: + and ÷

Option 2: + and –

Option 3: × and +

Option 4: ÷ and –

Correct Answer: + and ÷

Solution : Given:
(75 + 15) × 27 × 1 – 9 ÷ 7 × (135 + 3) – 10 ÷ (189 + 63) = 434

Apply the changes according to the given options, to balance the equation.
Let's check the options –
First option: + and ÷
⇒ (75 ÷ 15) × 27 × 1 – 9 + 7 × (135 ÷ 3) – 10 + (189 ÷ 63) = 434
(5) × 27 × 1 – 9 + 7 × (45) – 10 + (3) = 434
135 – 9 + 315 – 10 + 3 = 434
434 = 434
Second option: + and –
⇒ (75 – 15) × 27 × 1 + 9 ÷ 7 × (135 – 3) + 10 ÷ (189 – 63) = 434
(60) × 27 × 1 + 9 ÷ 7 × (132) + 10 ÷ (126) = 434
1620 + 1.28 × 132 + 0.079 = 434
1620 + 168.96 + 0.079 = 434
1789.03 ≠ 434
Third option: × and +
⇒ (75 × 15) + 27 + 1 – 9 ÷ 7 + (135 × 3) – 10 ÷ (189 × 63) = 434
(75 × 15) + 27 + 1 – 9 ÷ 7 + (135 × 3) – 10 ÷ (189 × 63) = 434
1125 + 27 + 1 – 9 ÷ 7 + 405  – 10 ÷ (11907) = 434
1125 + 27 + 1 – 1.2 + 405  – 0.00008 = 434
1556.79  ≠ 170
Fourth option: ÷ and –
⇒(75 + 15) × 27 × 1 ÷ 9 – 7 × (135 + 3) ÷ 10 – (189 + 63) = 434
(90) × 27 × 1 ÷ 9 – 7 × (138) ÷ 10 – (252) = 434
270 – 7 × 13.8 – 252 = 434
270 – 96.6 – 252 = 434
–78.6 ≠ 434

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