Solution:
Let x be the page required when report is retyped
Now, we can use work equivalence method
20 × 55 × 65 = 70 × 65 × x
Or, x = $$\frac{{20 \times 55 \times 65}}{{70 \times 65}}$$
Or, x = 15.70 = 16 pages.
Hence, % reduction in pages = $$\left( {20 - 16} \right) \times \frac{{100}}{{20}}$$   $$\, = \,$$ $$20\% $$

Solution:
$$\eqalign{ x\% {\text{ of }}a = y\% {\text{ of }}a \cr \Rightarrow \frac{x}{{100}}a = \frac{y}{{100}}b \cr \Rightarrow b = \left( {\frac{x}{y}} \right)a \cr \therefore z\% {\text{ of }}b: \cr = \left( {z\% {\text{ of }}\frac{x}{y}} \right)a \cr = \left( {\frac{{xz}}{{y \times 100}}} \right)a \cr = \left( {\frac{{xz}}{y}} \right)\% {\text{ of }}a \cr} $$

Solution:
x = 80% of y
⇒ x = $$\frac{80}{100}$$y
⇒ $$\frac{y}{x}$$ = $$\frac{5}{4}$$
⇒ $$\frac{y}{2x}$$ = $$\frac{5}{8}$$
∴ Required percentage :
$$\eqalign{ = \left( {\frac{y}{{2x}} \times 100} \right)\% \cr = \left( {\frac{5}{8} \times 100} \right)\% \cr = 62\frac{1}{2}\% \cr} $$

Solution:
Let the total number of applicants be $$x$$
Number of eligible candidates = 95 % of $$x$$
Eligible candidates of other categories
= 15% of (95 of $$x$$)
= $$\left( {\frac{{15}}{{100}} \times \frac{{95}}{{100}} \times x} \right)$$
= $$\frac{{57x}}{{400}}$$
∴ $$\frac{{57x}}{{400}}$$ = 4275
⇒ $$x$$ = $$\left( {\frac{{4275 \times 400}}{{57}}} \right)$$
⇒ $$x$$ = 30000

Solution:
Given:
Percentage increase in the price of diesel = 26%
Percentage increase in total expenditure = 15%
Concept used:
P × C = E
Where P is Price, C is Consumption and E is Expenditure
Calculation:
Let initial price be P₁, consumption be C₁, and expenditure be E₁
P₁ × C₁ = E₁
⇒ $${{\text{C}}_1} = \frac{{{{\text{E}}_1}}}{{{{\text{P}}_1}}}$$
Let new price be P₂, new quantity consumed be C₂, and new expenditure be E₂
P₂ = P₁ + 26% of P₁
⇒ P₂ = 1.26P₁
E₂ = E₁ + 15% of E₁
⇒ E₂= 1.15E₁
As, P₂ × C₂ = E₂
⇒ 1.26P₁ × C₂ = 1.15E₁
⇒ C₂ = $$\frac{{{\text{1}}{\text{.15}}{{\text{E}}_1}}}{{{\text{1}}{\text{.26}}{{\text{P}}_1}}}$$
⇒ C₂ = 0.9126 × $$\frac{{{{\text{E}}_1}}}{{{{\text{P}}_1}}}$$
⇒ C₂ = 0.9126C₁
Decrease in consumption = C₁ - C₂
⇒ Decrease in consumption = C₁ - 0.9126C₁ = 0.0874C₁
Percentage decrease in consumption = $$\frac{{{\text{Decrease in consumption}}}}{{{\text{Initial consumption}}}} \times 100$$
⇒ Percentage decrease in consumption = $$\frac{{0.0874{{\text{C}}_1}}}{{{{\text{C}}_1}}} \times 100$$
∴ The percentage decrease in consumption is 8.7% (correct to 1 decimal place)

Solution:
Given:
Salary of A is 30% more than salary of B
Calculation:
Let the salary of B be 100x
Salary of A = 100x + 100x × 30%
⇒ 130x
Percentage difference = $$\frac{{130{\text{x}} - 100{\text{x}}}}{{130{\text{x}}}} \times 100$$
= $$\frac{{30{\text{x}}}}{{130{\text{x}}}} \times 100$$
= 23.07% ≈ 23.1%
∴ B's salary is 23.1% less than that of A.

Solution:
$$\eqalign{ {\text{Let,}} \cr B = 110\% {\text{ of }}b = \frac{{11b}}{{10}}{\text{ }} \cr C = 110\% {\text{ of }}c = \frac{{11c}}{{10}} \cr D = 110\% {\text{ of }}d = \frac{{11d}}{{10}} \cr {\text{Then,}} \cr A = B \times \frac{D}{C} \cr A = \frac{{11b}}{{10}} \times \frac{{11d}}{{10}} \times \frac{{10}}{{11c}} \cr A = \frac{{11bd}}{{10c}} \cr A = \frac{{11}}{{10}}a \cr A = \frac{{110}}{{100}}a \cr A = 110\% {\text{ of }}a \cr \therefore {\text{ Increase }}\% = 10\% \cr} $$