Solution:
Let the weight of 1 student = x kg
The weight to 15 student = 15x kg
Let the weight of new comer = y kg
∴ According to the question,
⇒ 15x - 40 + y = 15 (x + 1.5)
⇒ 15x - 40 + y = 15x + 22.5
⇒ y = 62.5 kg

Solution:
Let the ratio be K : 1
Then,
⇔ K × 16.4 + 1 × 15.4 = (K + 1) × 15.8
⇔ (16.4 - 15.8) K = (15.8 - 15.4)
⇔ K = $$\frac{0.4}{0.6}$$
⇔ K = $$\frac{2}{3}$$
∴ Required ratio
= $$\frac{2}{3}$$ : 1
= 2 : 3

Solution:
Total age decreased
= (11 × 2) months
= 22 months
= 1 year 10 months
∴ Average age of two new players
$$\left( {\frac{{{\text{35 years 2 months}}}}{2}} \right)$$
= 17 years 7 months

Solution:
Let X be the number of employees.
We are given that 40% of the employees are workers.
Now, 40% of X is $$\frac{{40}}{{100}}$$ × X = 0.4X
Hence, the number of workers is $$\frac{{2{\text{X}}}}{5}$$
All the remaining employees are executives,
so the number of executives equals,
(The number of Employees) $$ - $$ (The number of Workers)
= X $$ - $$ $$\frac{{2{\text{X}}}}{5}$$
= $$\frac{{3{\text{X}}}}{5}$$
The annual income of each worker is Rs. 390.
Hence, the total annual income of all workers together is
= $$\frac{{2{\text{X}}}}{5}$$ × 390 = 156X
Also, the annual income of each executive is Rs.420.
Hence, the total income {of all the executives together is,
= $$\frac{{3{\text{X}}}}{5}$$ × 420 = 252X
Hence, the total income of the employees is,
= 156X + 252X = 408X
The average income of all the employees together = 408

Solution:
According to the question,
Average of whole class
$$\eqalign{ = \frac{{10 \times 12.5 + 20 \times 13.1}}{{30}} \cr = \frac{{125 + 262}}{{30}} \cr = \frac{{387}}{{30}} \cr} $$
= 12.9 years

Solution:
Let the five consecutive numbers be z, z + 1, z + 3 and z + 4
Then,
$$ \Rightarrow \frac{{z + \left( {z + 1} \right) + \left( {z + 2} \right) + \left( {z + 3} \right) + \left( {z + 4} \right)}}{5} = x$$
$$\eqalign{ \Rightarrow 5z + 10 = 5x \cr \Rightarrow z = \frac{{5x - 10}}{5} \cr \Rightarrow z = x - 2 \cr} $$
So, the numbers are x - 2, x - 1, x, x + 1, x + 2
∴ Required mean
$$ = \frac{{\left( {x - 2} \right) + \left( {x - 1} \right) + x + \left( {x + 1} \right) + \left( {x + 2} \right) + \left( {x + 3} \right) + \left( {x + 4} \right)}}{7}$$
$$\eqalign{ = \frac{{7x + 7}}{7} \cr = x + 1 \cr} $$

Solution:
Sum of ages of the captain and the youngest player
= [(28 × 11) - (25 × 3) + (28 × 3) + (30 × 3)] years
= (308 - 249) years
= 59 years
Let the age of the youngest player be x years.
Then, age of the captain = (x + 11) years
∴ x + (x + 11) = 59
⇒ 2x = 48
⇒ x = 24
So, the age of captain is
= (x + 11)
= (24 + 11)
= 35 years