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In the following question, two statements are numbered as A and B. On solving these statements we get quantities A and B respectively. Solve for the both quantities and choose the correct option. Quantity A: The average of a group of 9 numbers is 115. When a number is added to the group, the new average is 27 more than the number. Find the number. Quantity B: The average of a series of 8 numbers is 96. When two numbers are added to the series, the average is reduced by 3. If the difference between the numbers is 8, find the numbers.

In the following question, two statements are numbered as A and B. On solving these statements we get quantities A and B respectively. Solve for the both quantities and choose the correct option. Quantity A: The average of a group of 9 numbers is 115. When a number is added to the group, the new average is 27 more than the number. Find the number. Quantity B: The average of a series of 8 numbers is 96. When two numbers are added to the series, the average is reduced by 3. If the difference between the numbers is 8, find the numbers. Correct Answer 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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