Solution:
Total run till 10 overs is
= 3.2 × 10 = 32
Remaining runs
= 282 - 32 = 250
250 runs make in 40 overs so average runs per overs
= $$\frac{250}{40}$$
= 6.25

Solution:
Average age of 10 children = 9 years 9 months
Sum of ages of 10 children = 9 × 10 + $$\frac{9}{12}$$ × 10 = $$\frac{390}{4}$$
Average age of 9 children = 8 years 11 months
Sum of age of 9 children = 8 × 9 + $$\frac{11}{12}$$ × 9 = $$\frac{321}{4}$$
Age of 10th child
= $$\frac{390}{4}$$ - $$\frac{321}{4}$$
= $$\frac{69}{4}$$
= 17 years 3 months

Solution:
Max - Min = 172.....(i)
Max + Min = 50 × 40 - 48 × 38
Max + Min = 2000 - 1824
Max + Min = 176.....(ii)
From equation (i) and (ii)
Max = 174

Solution:
Let first odd number = a
Five odd number = a, a + 2, a + 4, a + 6, a + 8
= 5a + 2(1 + 2 . . . 4)
= 5a + 2$$\frac{{\left( 4 \right)\left( 5 \right)}}{2}$$
= 5a + 20
According to the question,
$$\frac{{5a + 20}}{5}$$ = 27
a + 4 = 27
a = 23
First number = 23
Last number = 23 + 8 = 31
Product of first and last number = 23 × 31 = 713

Alternate:
\[\begin{array}{*{20}{c}} {23}{25}{\boxed{27}}{29}{31} \\ \downarrow {} \downarrow {} \downarrow \\ {{\text{First Number}}}{}{{\text{Average}}}{}{{\text{Last Number}}} \end{array}\]
Average is middle term if common difference between them is same.
Product = 23 × 31 = 713

Solution:
Average weights of 21 boys = 64 kg
Total weights of 21 boys
= 64 × 21
= 1344 kg
The weight of the teacher was added then average increase by 1 kg
⇒ Total weight of teacher and 21 boys
= 65 × 22
= 1430 kg
∴ Weight of teacher
= 1430 - 1344
= 86 kg

Solution:
Let per day income of boy, women, man are = x, x + 10, x + 20
According to the question,
$$ \Rightarrow \frac{{7M + 11W + 2B}}{{20}}$$    = 257.50
$$ \Rightarrow 7\left( {x + 20} \right) + 11\left( {x + 10} \right) + 2x$$       = 257.50 × 20
$$ \Rightarrow 7x + 140 + 11x + 110 + 2x$$       = 5150
$$\eqalign{ \Rightarrow 20x = 5150 - 250 \cr \Rightarrow x = \frac{{4900}}{{20}} \cr \Rightarrow x = 245 \cr} $$
Per day income of man
= x + 20
= 245 + 20
= 265

Solution:
Age of the instructor
= (34 × 11 - 32 × 10) years
= (374 - 320) years
= 54 years