Mean of 10 observations (numbers) is 20. If one number is included, the mean becomes 21, the included number is :

1. 431

2. 31

3. 231

4. 131

Given:

Number of observations = 10

Mean = 20

Let a be the sum of all observations.

Mean = $\dfrac{\text{Sum of all observations }}{\text{Number of all observations }}$

⇒ 20 = $\dfrac{a}{10}$

⇒ 20 x 10 = a

⇒ 200 = a

Let b be the number added to the observation.

New mean = 21

New mean = $\dfrac{\text{Sum of all old observations + b}}{\text{Number of all old observations + 1}}$

⇒ 21 = $\dfrac{200 + \text{b}}{11}$

⇒ 21 x 11 = 200 + b

⇒ 231 = 200 + b

⇒ b = 231 - 200

⇒ b = 31

Hence, option 2 is the correct option.