According to the question,
a × $$\frac{x}{100}$$ = b × $$\frac{y}{100}$$
xa = yb
⇒ b = $$\frac{xa}{y}$$
Put value of b in given equation,
z% of b = z% of $$\frac{xa}{y}$$ = $$\frac{zx}{y}$$ of a

Let the maximum marks = x
According to the question,
Case (i) pass marks = $$\frac{20x}{100}$$ + 30
Case (ii) pass marks = $$\frac{32x}{100}$$ - 42
Note : Pass marks would be same in both cases.
$$\frac{20x}{100}$$ + 30 = $$\frac{32x}{100}$$ - 42
$$\frac{12x}{100}$$ = 72
x = 600
Pass marks :
= 600 × $$\frac{20}{100}$$ + 30
= 150
Required percentage :
= $$\frac{150}{600}$$ × 100
= 25%

x × $$\frac{20}{100}$$ × $$\frac{20}{100}$$ = 16000
x = 400000

After increment of 6% new length of AC
= 3 + $$\frac{3 × 6}{100}$$ = 3.18cm
Required % decrease
= $$\frac{0.18}{2}$$ × 100
= 9%

Percentage of Non-tax paying employees
= (100 - 31)%
= 69%
69% of total employees = 20700
Total employees
= $$\frac{20700}{69}$$ × 100
= 30000

Total votes = 104000
Total valid votes :
= 104000 × $$\frac{(100 - 2)}{100}$$
= 104000 ×$$\frac{98}{100}$$
= 101920
Votes polled in favour of the candidate :
= 101920 × $$\frac{55}{100}$$
= 56056

Percentage of failed students = 25%
∴ Percentage of passed students
= (100 - 25)% = 75%
According to the question,
Total students :
= $$\frac{450}{75}$$ × 100 = 600

1^st number : 2^nd number
           5     :     4
40% = $$\frac{2}{5}$$
2 units = 12
5 units = 30
So, 1^st number = 30
2^nd number = $$\frac{30}{5}$$ × 4 = 24
50% of 2^nd = 24 × $$\frac{1}{2}$$ = 12

Number of a boy in the school = 720 × $$\frac{7}{12}$$   = 420
Number of a girl in the school = 720 × $$\frac{5}{12}$$   = 300
To maintain 1 : 1 we will have to add number of girls = 420 - 300 = 120

Sugar in original solution = $$\frac{{75 \times 30}}{{100}}$$  = 22.5 gm
Let m gm of sugar be mixed.
$$\therefore \frac{{22.5 + {\text{m}}}}{{75 + {\text{m}}}} \times 100 = 70$$
⇒ 2250+ 100m = 75 × 70 + 70m
⇒ 2250 + 100m = 5250 + 70m
⇒ 30m = 5250 - 2250 = 3000
⇒ m = $$\frac{{3000}}{{30}}$$  = 100 gm

Let the number of boys is = 8x
Number of girls = 12x
Boys are not getting scholarship
= 8x × $$\frac{1}{2}$$ = 4x
Girls are not getting scholarship
= 12x × $$\frac{3}{4}$$ = 9x
% of students not getting scholarship
= $$\frac{(4x + 9x)}{20x}$$   × 100
= 65%

The number of failure boys
= $$\frac{640 × 40}{100}$$
= 256
The number of failure girls
= $$\frac{360 × 20}{100}$$
= 72
Percentage of failure students
= $$\frac{(72 + 256)}{640 + 360}$$
= 32.8%

Total number boy = 1100 and girl = 900
Total number of boy fail (50%) = 550
Total number of girl fail ( 60%) = 540
Total failed candidates = (550 + 540) = 1090
Required percentage of failed candidates :
= $$\frac{1090}{(1100 + 900)}$$   × 100
= $$\frac{1080 × 100}{2000}$$
= 54.5%

Let a total of 5x match is played between Pakistan and India. Pakistan won 3x matches and India won 2x matches
According to the question,
But now India won 30 matches in a row and hence India's success percentage increase to 70%.
Now, Total match = 5x + 30
(2x + 30) = (5x + 30) × $$\frac{70}{100}$$
20x + 300 = 35x + 210
15x = 90
x = 6
So, total match :
= 5x + 30
= 5 × 6 + 30
= 60 matches

$$66\frac{2}{3}$$% = $$\frac{2}{3}$$
Let the income of the person = 3 units
Expenditure = 2 units
Savings = (3 - 2) = 1 unit
According to the question,
1 unit = Rs. 1200
2 units = 2 × 1200 = Rs. 2400

Total valid votes got candidates
= $$\frac{9261}{75}$$ × 100
= 12348
Let total number of votes = x
Total votes polled
= x × $$\frac{75}{100}$$
= $$\frac{75x}{100}$$
Valid votes = $$\frac{75x}{100}$$ × $$\frac{98}{100}$$
According to the question,
⇔ $$\frac{75x}{100}$$ × $$\frac{98}{100}$$ = 12348
⇔ x = 16800
Hence, total votes = 16800

40% = $$\frac{{2\,\, \to \,\,{\text{Alcohol}}}}{{5\,\, \to \,\,{\text{Mixture}}}}$$
Water : Alcohol
     3   :   2
Required percentage
= $$\frac{2}{(5 + 1)}$$ × 100
= $$\frac{2}{6}$$ × 100
= $$\frac{1}{3}$$ × 100
= $$33\frac{1}{3}$$%

Let the number be x
According to the question,
x + 320 × $$\frac{10}{100}$$ = 230 × $$\frac{30}{100}$$
x + 32 = 69
x = 37
Hence, required number = 37

120 × $$\frac{25}{100}$$ + 380 × $$\frac{40}{100}$$ = x × 637
⇒ 30 + 152 = x × 637
⇒ $$\frac{182}{637}$$ = x
⇒ x = $$\frac{2}{7}$$
⇒ Required answer = $$\frac{2}{7}$$

Let the number = x
According to the question,
x - 15 = $$\frac{80x}{100}$$
x - 15 = $$\frac{4x}{5}$$
5x - 75 = 4x
x = 75
Required answer
= 75 × $$\frac{40}{100}$$
= 30

Let the total number of the voter is 100x and the winner get 60x votes and loser get 40x votes.
∴ According to question
60x - 40x = 298
⇒ x = $$\frac{298}{20}$$
∴ Total Number of voter = 100 × $$\frac{298}{20}$$   = 1490

Let conside 100 item sold on Rs.100
∴ Total Amount = 100 × 100 = Rs. 10000
Now After 20% discount price become Rs.80
Total Number of Sale increased after discount is 80%.
i.e.
100 + 80% of 100 = 180(Item sold)
∴ Total Amount = 180 × 80 = Rs. 14400

Increased in amount = 14400 - 10000 = 4400
% Increase in amount
= $$\frac{{4400 \times 100}}{{10000}} $$
= 44% (increase)

Failed students in Mathematics = 34%
Failed students in English = 42%
Student failed in both subject math and english = 20%
Student only fail in Math = 34 - 20 = 14%
Student only fail in English = 42 - 20 = 22%
Percentage of passed students in both subjects :
= 100 - [ student fail in maths + student fail in english + student fail in both subject]
= [100 - (14 + 20 + 22)]
= 44%

Total income = 100x
10% deposit to orphange = 100x of 10% = 10x
Remain income 90x
Now 20% deposit to bank = 90x of 20% = 18x
Reamin income 90x - 18x = 72x
According to question
72x = 7200
⇒ x = $$\frac{7200}{72}$$ = 100
Income of Christy = 100 × 100 = 10000

% increase = 10 + 10 + $$\frac{10 × 10}{100}$$  = 21%
Total increase = $$\frac{100 × 21}{100}$$  = Rs. 21

Let the original price = 100x
Article price 1st increased by 10%. i.e price of article become 100x + 100x of 10% = 110x
And then the article price increased by 20% i.e. price of article become 110x + 110x of 20% = 132x
According to the question,
132x = 33
⇒ x = $$\frac{33}{132}$$
⇒ x = $$\frac{1}{4}$$
Therefore Original price of Article is
= 100 × $$\frac{1}{4}$$
= Rs. 25

Gain in price = 7.5 - 6 = 1.5
Required percentage reduction
= $$\frac{1.5}{7.5}$$ × 100
= 20%

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

20% = $$\frac{1}{5}$$ = $$\frac{{6\,\, \to \,\,{\text{Girls}}}}{{5\,\, \to \,\,{\text{Boys}}}}$$
Boys : Girls
5 : 6
According to the question,
(5 + 6) units = 66
11 units = 66
1 unit = 6
Hence Boys = 6 × 5 = 30
           Girls = 6 × 6 = 36
The number of girls when 4 is admitted
= (36 + 4)
= 40
Required ratio :
= 30 : 40
= 3 : 4

According to the question,
P × $$\frac{P}{100}$$ = 36
⇒ P² = 3600
⇒ P = 60