Let average age of whole team by x years
? 11x - (26 + 29) = 9(x - 1)
? 11x - 9x = 46
? 2x = 46
? x = 23
So, average age of team is 23 years

Arithmetic mean
$$\frac{{{\text{Total sum}}}}{{{\text{Total number}}}}$$
According to question,
? 10 = $$\frac{7 + 5 + 13 + x + 9}{5}$$
? 50 = x + 34
? x = 50 - 34
? x = 16

Let Ajit's average be x for 9 innings. So, Ajit scored 9x run in 9 innings.
In 10^th inning, he scored 100 runs n average became (x+8). And he scored (x + 8) × 10 runs in 10 innings.
Now,
$$\eqalign{ & \Rightarrow 9x + 100 = 10 \times \left( {x + 8} \right) \cr & {\text{or}},\,9x + 100 = 10x + 80 \cr & {\text{or}},\,x = 100 - 80 \cr & {\text{or}},\,x = 20 \cr & {\text{New}}\,{\text{average}} = \left( {x + 8} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 28\,{\text{runs}} \cr} $$

Let 10 numbers be x1, x2, x3, . . . . . . . x10
According to question average of se 10 numbers is 10
$$ \Rightarrow \frac{{ {x1 + x2 + x3 + .... + x10} }}{{10}} = x$$
Now if each number is increased by 10%,
n new average, say y.
$$y = \frac{{ {1.1x1 + 1.1x2 + 1.1x3 + .... + 1.1x10} }}{{10}}$$
$${\kern 1pt} \Rightarrow y = 1.1 \times {\frac{{ {x1 + x2 + x3 + .... + x10} }}{{10}}} $$
$$\eqalign{ & \Rightarrow y = 1.1x \cr & \Rightarrow y\,{\text{is }}10\% \,{\text{increased}} \cr} $$

$$\eqalign{ & {\text{Let}}\,{\text{}}\,{\text{three}}\,{\text{numbers}}\,{\text{be}}\,x,\,y,\,{\text{and}}\,z.\, \cr & {\text{We}}\,{\text{are}}\,{\text{given}}\,{\text{that}}\, \cr & \frac{{ {x + y} }}{2} = 2 \cr & \frac{{ {y + z} }}{2} = 3 \cr & \frac{{ {x + z} }}{2} = 4 \cr & {\text{Adding}}\,{\text{three}}\,{\text{equations}}, \cr & \frac{{ {x + y} }}{2} + \frac{{ {y + z} }}{2} + \frac{{ {x + z} }}{2} = 2 + 3 + 4 \cr & x + y + z = 9 \cr & {\text{The}}\,{\text{average}}\,{\text{of}}\,{\text{}}\,{\text{three}}\,{\text{numbers}}\,{\text{is}}, \cr & \frac{{ {x + y + z} }}{3} = \frac{9}{3} = 3 \cr} $$

According to question,
? Total temperature of first four days
Mon + Tue + Wed + Thu
= 25 × 4 = 100°C.....(i)
? Total temperature of last four days
Thu + Fri + Sat + Sun
= 25.5 × 4 = 102°C .....(ii)
? Total temperature of week
= 25.2 × 7 = 176.4°C .....(iii)
After adding equation (i) + (ii)
Mon + Tue + Wed + 2 × Thu + Fri + Sat + Sun
= 100° + 102° = 202°C.....(iv)
After subtracting equation (iv) - (iii)
= 202° - 176.4° = 25.6° C
? Temperature of 4th day = 25.6° C

Let total number of workers be x.
Then,
? 8000x = (12000 × 7) + 6000(x - 7)
? 2000x = 42000
? x = 21

Let Arun's weight by X kg.
According to Arun,
65 < X < 72
According to Arun's bror,
60 < X < 70
According to Arun's mor,
X $$ \leqslant $$ 68
The values satisfying all above conditions are 66, 67 and 68.
Required average,
$$\eqalign{ & = \frac{{66 + 67 + 68}}{3} \cr & = \frac{{201}}{3} \cr & = 67\,{\text{kg}}{\text{.}} \cr} $$

Let A, B, C represent ir respective weights. Then, we have:
A + B + C = (45 x 3) = 135 .... (i)
A + B = (40 x 2) = 80 .... (ii)
B + C = (43 x 2) = 86 ....(iii)
Adding (ii) and (iii), we get: A + 2B + C = 166 .... (iv)
Subtracting (i) from (iv), we get : B = 31
Therefore B's weight = 31 kg.

Let average age of whole team be x years.
? 11x - (26 + 29) = 9 (x - 1)
? 11x - 9x = 46
? 2x = 46
? x = 23
So, average age of team is 23 years.