Which of the numbers(not digits) should be interchanged in the below equation to make it mathematically correct?

216 ÷ 9 × 16 + 24 - 27 = 126

This question was previously asked in
SSC GD Constable (2022) Official Paper (Held On : 30 Jan 2023 Shift 2)
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  1. 16 and 9
  2. 27 and 9
  3. 24 and 27
  4. 9 and 24

Answer (Detailed Solution Below)

Option 4 : 9 and 24
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Detailed Solution

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1. 16 and 9

216 ÷ 16 × 9 + 24 - 27 = 126

13.5 × 9 + 24 - 27 = 126

121.5 + 24 - 27 = 126

145.5 - 27 = 126

⇒ 118.5  126

2. 27 and 9

216 ÷ 27 × 16 + 24 - 9 = 126

8 × 16 + 24 - 9 = 126

128 + 24 - 9 = 126

152 - 9 = 126

⇒ 143 ≠ 126

3. 24 and 27

216 ÷ 9 × 16 + 27 - 24 = 126

24 × 16 + 27 - 24 = 126

384 + 27 - 24 = 126

411 - 24 = 126

⇒ 387 ≠ 126

4. 9 and 24

216 ÷ 24 × 16 + 9 - 27 = 126

9 × 16 + 9 - 27 = 126

144 + 9 - 27 = 126

153 - 27 = 126

⇒ 126 = 126

Hence, '9 and 24' is the correct answer.

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