Let the maximum marks be x.
Now, 80% of x = 576
\(\frac { 80 }{ 100 } \)\(\times\) x = 576
⇒ x = 576 x \(\frac { 100 }{ 10 } \)
x = 720 marks
Therefore, the total marks in the examination = 720.

Let the total votes polled be x.
Votes polled in favour in A = 58% of x =\(\frac { 58x }{ 100 } \)
Votes polled in favour of B = (100 − 58)% of x = 42% of x = \(\frac { 42x }{ 100 } \)
Given, Winning margin A− B = 192
That is, \(\frac { 58x }{ 100 } \)- \(\frac { 42x }{ 100 } \) = 192
⇒\(\frac { 16x }{ 100 } \)=192
x = 192 x \(\frac { 100 }{ 16 } \)
x = 1200 votes

x% of 600 = 450
\(\frac { x }{ 100 } \)× 600 = 450
\(x=\frac { 450 }{ 6 } \)
x = 75

The given two successive discounts are 10% and 20%
The amount to be paid by the customer
\(=\frac{90}{100} \times \frac{80}{100} \times 7500=5400\)
The customer has to paid = Rs. 5400

(i) M.P of the book = Rs. 225
S.P of the book = x
Discount = 8% 
S.P of the book = M.p - Discount
= 225 - 8% of 225
\(=225-\frac{8}{100} \times 225\)
= 225 - 18 = Rs.207
S.P of the book = Rs. 207
(ii) M.P of the LED TV = y
S.P of the LED TV = Rs. 11970
Discount = 5%
11970 - y- 5% of  y
\( 11970 =\mathrm{y}-\frac{5}{100} \mathrm{y} \)
\(11970 =\frac{95 \mathrm{y}}{100} \)
\(11970 =\frac{19 \mathrm{y}}{20} \)
\(\mathrm{y} =\frac{11970 \times 20}{19}=12,600 \)
M.P of the LED TV = Rs. 12,600
(iii) M.P of the Digital clock = Rs. 750
S.P of the Digital clock = Rs. 615
Discount = z
Discount = M.P - S.P
= 754 -615 = 135
z % of 750 = 135 
\( \frac{z}{100} \times 750 =135 \)
\(\frac{15 z}{2} =135 \)
\(z =\frac{135 \times 2}{15}\)
Discount = 18%

We know that if the,cost price of x articles = selling price of y articles, then
\( \text { Profit } \% =\left(\frac{x-y}{y} \times 100\right) \% \)
\(=\left(\frac{15-10}{10} \times 100\right) \% \)
\(=\frac{5}{10} \times 100 \%=50 \%\)

Let x be the cost price of the article.
810 - x = x - 530
2x = 810 + 530
2x = 1340
x = 670
The cost price of the article is Rs. 670.

The ratio of loys and girls = 5 : 3
16% of boys and 8% of girls failed.
84% of boys and 90% of girls passed.
The percentage of passed students
\(\text { boys passed } 84 \% \text { of } \frac{5}{8}+\text { girls passed } 92 \% \text { of } \frac{3}{8}\)
\( =\frac{84}{100} \times \frac{5}{8}+\frac{92}{100} \times \frac{3}{8} \)
\(=\frac{21}{40}+\frac{69}{200} \)
\(=\frac{105+69}{200} \)
\(=\frac{174}{200}=\frac{87}{100} \)
= 87%
The percentage of passed students = 87%

Let the numerator be x and the denominator be y.
The original fraction = x/y
Given the numerator of a fraction is increased by 50%
\( \therefore \mathrm{Nr} =x+50 \% \text { of } x \)
\(=x+\frac{50}{100} x=x+\frac{1}{2} x \\ \mathrm{Nr} =\frac{3}{2} x \)
Also given the denominator is decreased by 20 %
\( \text { Dr } =y-20 \% \text { of } y \)
\(=y-\frac{20}{100} y=y-\frac{1}{5} y=\frac{4}{5} y \)
By given data
\( \frac{\frac{3}{2} x}{\frac{4}{5} y}=\frac{3}{5} \Rightarrow \frac{3}{2} x \times \frac{5}{4 y}=\frac{3}{5} \)
\(\frac{x}{y}=\frac{8}{25} \)
The original fraction is 8/25

Let the number be x.
Given: x - 2 % of x = 80
\( x-\frac{20}{100} \times x=80 \)
\(x\left(1-\frac{20}{100}\right) =80 \)
\(x\left(\frac{80}{100}\right) =80 \)
\(\therefore x =\frac{80 \times 100}{80}\)
x = 100
The required number is 100.

Decrease value = Original price - Sold Price
= Rs. 3,00,00 - 2,00,00
= Rs. 1,00,000
\(\therefore \text { Percentage of decrease }=\frac{100000}{300000} \times 100\)
\(=33 \frac{1}{3} \%\)

25% of 30% of 400
\(=25 \% \text { of }\left(\frac{30}{100} \times 400\right)\)
= 25% of 120
\(=\frac{25}{100} \times 120=30\)
25% of 30% of 400 = 30

Let the number be x.
\( \frac{32}{100} \times x =48 \)
\(x =\frac{48 \times 100}{32}=150\)
The number is 150

(i) \(\text { one half }=\frac{1}{2} \times 100 \%=50 \%\)
(ii) \(\frac{7.5}{10} \times 100 \%=75 \%\)
(iii) The word pure means 100%
(iv) \(\frac{48}{50} \times 100 \%=96 \%\)
(v) \(\frac{2}{3} \times 100 \%=66 \frac{2}{3} \%\)

Let the marked price be Rs x.
Now, x + \(\frac { 18x }{ 100 } \) = 10502
\(\frac { 118x }{ 100 } \) = 10502
∴ Marked price, x = Rs. 8900.
GST at 18% = 8900 x \(\frac { 18 }{ 100 } \)
= Rs. 10502 – Rs. 8900
= Rs.1602

Marked price = Rs. 550 and Discount = 8%
∴ Discount = \(\frac { 8 }{ 100 } \)x 550 = Rs. 44
∴ Selling Price = Marked price – Discount
= Rs. 550 − 44
= Rs. 506
∴ The selling price of the tube light is Rs. 506