Marked price of the shirt = Rs 850
Selling price of the shirt = Rs 765
\(\therefore\) Discount = [Marked price] - [Selling price]
= Rs 850 - Rs 765 = Rs 85
Now, d.iscount per cent =\({85\over 850}\times 100\%=10\%\)

Rs 3456

Rs 380

Given ratio = 2 :3
∴ Percentage =\((\frac{2}{3}\times100)=(\frac{200}{3})=66\frac{2}{3}\)%

Let the total number of students be x. Then, 40% of x are girls.
Therefore, 40% of x = 20 \(\Rightarrow \frac{40}{100}\times x\) = 20 \(\Rightarrow x=\frac{20\times100}{40}=50\)
So, the number of boys = 50 - 20 =30
Ratio of number of girls to the number of boys = 20 : 30 = \(\frac{20}{30}=\frac{2}{3}\)
Hence,\(\frac{2}{3}\)is written as 2: 3 and read as 2 is to 3.

In case of Fabina,
principal (P₁) = Rs 12500, rate (R₁ ) =12%, time (T₁ ) =3 yr
∴ Simple interest=\(\frac{P_1\times R_1\times T_1}{100}=\frac{12500\times12\times3 }{100}\)
= 125ｘ12ｘ3 = Rs 4500
In case of Radha,
Principal (P₂) =Rs 12500, Rate (R₂) =10%, Time (n) =3 yr
∴ Amount (A) = P₂\((1+\frac{R_2}{100})=12500(1+\frac{10}{100})^{3}\)
= 12500\((\frac{100+10}{100})^{3}=12500(\frac{110}{100})^{3}\)
= 12500\((\frac{11}{10})^{3}=12500\times \frac{11}{10}\times \frac{11}{10}\times \frac{11}{10}\)
= \(\frac{25\times 11\times 11\times 11}{2}=\frac{33275}{2}\)= Rs 16637.50
ஃ Compound interest =Amount (A) - Principal (P)
= Rs (16637.50 -12500) =Rs 4137.50
Hence, Fabina has to pay more interest at
Rs (4500-4137.5) i.e. Rs 362.50. 

10%

Let Chameli had total money be Rs x.
Percentage of money spent by Chameli = 75%
Chameli had left money after spending = (100 - 75)%
= 25%
But money left = Rs 600             [given]
∴ 25% of x = 600
⇒ \(\frac{25}{100}\times x=600 \Rightarrow x=\frac{600\times100}{25}=2400\)
Hence, Chameli had Rs 2400 in the beginning.
 Alternate Method
Let total money with Chameli at the beginning be Rs 100.
Expenditure money = 75% of total money
\(= Rs(\frac{75}{100}\times100)=Rs 75\)
Money left = Rs 100 - Rs 75=Rs 25
Now, if saving is Rs 25, then money at the beginning = Rs 100 
If saving is Rs 1, then money at the beginning = Rs \(\frac{100}{25}\)
If saving is Rs 600, then money at the beginning
\(= Rs (\frac{100}{25}\times 600)=Rs(4\times 600)= Rs 2400\)
Hence, total money at the beginning with Chameli was Rs 2400.

(i) Here, 90 parents helped their children for \(\frac{1}{2}\)h to 1\(\frac{1}{2}\) h.
Given, percentage = 30%
Let x parents be surveyed.
Then, 30% of x helped for \(\frac{1}{2}\)h to 1\(\frac{1}{2}\)h = 90
∴ 30% of x = 90
⇒ \(\frac{30}{100} \times x=90\)
⇒ \(x=\frac{90\times100}{30}=300\)
Hence, the number of parents were 300.
(ii) Here, 50% parents did not help at all.
So, number of parents did not help = 50% of 300
= \(\frac{50}{100}\times100=50\times3=150\)
Hence, 150 parents did not help.
(iii)Here, 20% parents helped for more than 1\(\frac{1}{2}\)h.
So, number of parents who helped for more than 1\(\frac{1}{2}\)h
= 20% of 300=\(\frac{20}{100} \times300=20\times3\)
= 60
Hence, 60 parents helped for more than  1\(\frac{1}{2}\)h.

Area of floor = (6 x 3)m² = 18m²
Area covered by carpet = 8 m²
When 18m² area will covered by carpet, then floor will be covered = 100%
or when 1m² area covered by carpet. then floor will be covered =\(\frac{100}{18}\)%
So, when 8m² area covered by carpet, then floor will be covered =\((\frac{100}{18}\times 8)\)% = 44.44%

For population in 2005, i.e. 2 yr after 2003,
Initial population = 54000, i.e. in the year 2003
Time (n) = 2 year, Rate of increase = 5%
Let population in 2005 be A.
∴ \(A=P(1+\frac{R}{100})^{n}=54000(1+\frac{5}{100})^{2}\)
= \(54000(\frac{100+5}{100})^{2}=54000(\frac{105}{100})^{2}\)
= \(54000\times \frac{105}{100}\times \frac{105}{100}=27\times21\times21\times105\) = 59535
Hence, the population in 2005 is 59535.

The price includes the VAT (The Value Added Tax). A 10% VAT means, if the price without VAT is Rs 100, then
price including VAT is RS. 110.
Now, when price including VAT is Rs 110, original price is Rs 100.
Hence, when price including tax is 3300, the original price = Rs \(\frac{100}{110}\times 3300\)=Rs 3000

We know that,
Discount = Marked price - Sale price
Sale price = Marked price - Discount
∵ Marked price = Rs 650                   [given]
Discount = 10% of Rs 650 =\(\frac{10}{100}\times 650\)=65
∴ Sale price = Marked price - Discount = Rs (650 - 65) = Rs 585

7%