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Option 3 : Quantity A ≥ Quantity B
Solving for Quantity A:
Let the number be ‘x’
Sum of 9 numbers = 9 × 115 = 1035
When the number is added, sum of 10 numbers = 1035 + x
Average of 10 numbers = 27 + x
⇒ 10(27 + x) = 1035 + x
⇒ 270 + 10x = 1035 + x
⇒ 9x = 765
⇒ x = 765/9 = 85
⇒ Quantity A = 85
Solving for Quantity B:
Let the numbers be ‘x’ and ‘(x + 8)’
Sum of 8 numbers = 8 × 96 = 768
Sum of 10 numbers = 768 + x + x + 8 = 776 + 2x
Average of 10 numbers = 96 - 3 = 93
⇒ 776 + 2x = 10(93)
⇒ 2x = 930 - 776
⇒ x = 154/2 = 77
⇒ x + 8 = 77 + 8 = 85
⇒ Quantity B = 77, 85
∴ Quantity A ≥ Quantity B
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