The mean of observations, given in the adjoining table, is 24, the value of a is :

x	f
10	10
20	a
30	30

1. 20

2. 30

3. 10

4. 25

By formula,

Mean = $\dfrac{Σfx}{Σf}$

Substituting values we get :

$\Rightarrow 24 = \dfrac{1000 + 20a}{40 + a}$

⇒ 24(40 + a) = 1000 + 20a

⇒ 960 + 24a = 1000 + 20a

⇒ 24a - 20a = 1000 - 960

⇒ 4a = 40

⇒ a = $\dfrac{40}{4}$

⇒ a = 10

∴ Value of a = 10

Hence, option 3 is the correct option.