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Mathematics

Assertion (A) : The mean age of nine boys is 28 years. If one new boy joins them, new mean age becomes 29 years. The age of new boy is (29 - 28) × 10 years.

Reason (R) : The age of new boy is 29 × 10 - 28 × 9 years.

  1. A is true, R is false.

  2. A is false, R is true.

  3. Both A and R are true.

  4. Both A and R are false.

Statistics

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Answer

Given,

The mean age of nine boys is 28 years.

⇒ Mean age = Total ageNo. of boys\dfrac{\text{Total age}}{\text{No. of boys}}

⇒ 28 = Total age9\dfrac{\text{Total age}}{9}

⇒ Total age = 28 × 9.

Given,

If one new boy joins them, new mean age becomes 29 years.

⇒ Mean age = New total ageNo. of boys\dfrac{\text{New total age}}{\text{No. of boys}}

⇒ 29 = New total age10\dfrac{\text{New total age}}{10}

⇒ New total age = 29 × 10.

Age of new boy = New total age - Total age = 29 × 10 - 28 × 9.

∴ Assertion (A) is false and Reason (R) is true.

Hence, Option 2 is the correct option.

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