Solution:
Let Raman's expense be Rs. $$x$$
Then, Vimal's expenses :
= 90% of $$x$$
$$\eqalign{ = {\text{ Rs}}{\text{. }}\left( {\frac{{90}}{{100}} \times x} \right) \cr = {\text{Rs}}{\text{. }}\frac{9}{{10}}x{\text{ }} \cr} $$
Aman's expense :
$$\eqalign{ = {\text{130% of Rs}}{\text{. }}\left( {\frac{{9x}}{{10}}} \right) \cr = {\text{ Rs}}{\text{. }}\left( {\frac{{130}}{{100}} \times \frac{{9x}}{{10}}} \right) \cr = {\text{ Rs}}{\text{. }}\frac{{117x}}{{100}} \cr \therefore \frac{{117x}}{{100}} + \frac{{9x}}{{10}} + x = 6447 \cr \Rightarrow \frac{{117x + 90x + 100x}}{{100}} = 6447 \cr \Rightarrow 307x = 644700 \cr \Rightarrow x = \frac{{644700}}{{307}} \cr \Rightarrow x = 2100 \cr {\text{Hence, Aman's expenses :}} \cr = {\text{Rs}}{\text{. }}\left( {\frac{{117 \times 2100}}{{100}}} \right) \cr = {\text{Rs}}{\text{. 2457}} \cr} $$

Solution:
Let the number is = x
According to the question,
$$\frac{1}{5}$$ of $$\frac{1}{2}$$ of x = 20
$$\frac{1}{5}$$ × $$\frac{1}{2}$$ × x = 20
x = 200
∴ 20% of 200 :
= $$\frac{20}{100}$$ × 200 = 40

Solution:
Let the total number of votes polled be x
Then, votes polled by other candidate
= (100 - 62)% of x
= 38% of x
∴ 62% of x - 38% of x = 432
⇒ $$\frac{24x}{100}$$ = 432
⇒ x = $$\frac{432 × 100}{24}$$
⇒ 1800

Solution:
$$\eqalign{ {\text{Let total numbe of oranges}} = x \cr \left\{ {\left( {\frac{{x \times 55}}{{100}} - 1} \right) \times \frac{{80}}{{100}} - 2} \right\} \times \frac{{10}}{{100}} = 5 \cr \left( {\frac{{x \times 55}}{{100}} - 1} \right) \times \frac{{80}}{{100}} = 50 + 2 \cr \left( {\frac{{x \times 55}}{{100}} - 1} \right) = \frac{{52 \times 10}}{8} \cr \frac{{x \times 55}}{{100}} - 1 = 65 \cr \frac{{x \times 55}}{{100}} = 66 \cr x = \frac{{66 \times 100}}{{55}} \cr x = 120 \cr} $$

Solution:
Given:
A, B, and C spend 80%, 85%, and 75% of their incomes respectively.
Savings are in the ratio 8 : 9 : 20 respectively.
Difference between the income of A and C is Rs. 18,000.
Concept used:
Income - Expenditure = Savings
Calculation:
A, B and C spend 80%, 85% and 75% of their incomes respectively.
Out of 100%, A spend 80%,
Income : Expenditure = 100 : 80 = 5 : 4,
Out of 100%, B spend 85%,
Income : Expenditure = 100 : 85 = 20 : 17,
Out of 100%, C spend 75%,
Income : Expenditure = 100 : 75 = 4 : 3,
Ratio Income : Expenditure is 5 : 4, 20 : 17, 4 : 3 respectively.
Savings = Income - Expenditure
Savings of A : B : C = (5 - 4) : (20 - 17) : (4 - 3)
Savings of A : B : C = 1 : 3 : 1
According to the question,
Savings are in the ratio 8 : 9 : 20 respectively.
Adjusting the savings ratio,
⇒ Savings = 1 × 8 : 3 × 3 : 1 × 20 = 8 : 9 : 20
⇒ Income = 5 × 8 : 20 × 3 : 4 × 20 = 40 : 60 : 80
⇒ Expenditure = 4 × 8 : 17 × 3 : 3 × 20 = 32 : 51 : 60
According to the question,
Income of C - Income of A = 18,000
⇒ 80 - 40 = 18,000
⇒ 1 unit = $$\frac{{18,000}}{{40}}$$  = 450
Income of B = 60 unit
⇒ 60 × 450 = Rs. 27,000
∴ The income of B is Rs. 27,000.

Solution:
$$\frac{4}{5}$$ × 70 = 56 and $$\frac{5}{7}$$ × 112 = 80
∴ Required percentage :
$$\eqalign{ = \left( {\frac{{80 - 56}}{{80}} \times 100} \right)\% \cr = \left( {\frac{{24}}{{80}} \times 100} \right)\% \cr = 30\% \cr} $$

Solution:
Let A salary's in starting is = 100
Now after decreased by 50% A salary become = 50
Again 50% of salary increase i.e. 50% of 50 = 25
Current salary is = 50 + 25 = 75
Actual decrease in salary of A = 100 - 75 = 25
Actual % lose = $$\frac{25}{100}$$ × 100 = 25%