Question

The mean age of nine boys is 28 years and if one new boy joins them the mean age increases by one.

Assertion (A): The age of new boy is (29 × 10 − 28 × 9) years.

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

पर्याय

• A is true, R is false.

• A is false, R is true.

• Both A and R are true and R is the correct reason for A.

• Both A and R are true and R is the incorrect reason for A.

Answer 1

A is true, R is false.

Explanation:

Given, the mean age of 9 boys is 28 years.

when one new boy joins, the mean age increases by 1 year, making the new mean 29 years

By formula,

Mean = `"Sum of all observations"/"Number of all observations"`

The mean age of 9 boys is 28 years.

⇒ Mean = `"Sum of ages of 9 boys"/9`

⇒ `28 = ("Sum of ages of 9 boys")/9`

⇒ Sum of ages of the boys = 28 × 9

After the new boy joins, the mean age becomes 29 years for 10 boys.

⇒ `29 = "Sum of ages of 10 boys"/10`

⇒ Sum of ages of 10 boys = 29 × 10

The age of the new boy is the difference between the total age of 10 boys and the total age of 9 boys = 29 × 10 − 28 × 9

∴ A is true, R is false.