\(\frac{4}{15}A = \frac{2}{5}B\)

\(\Rightarrow A =( \frac{2}{5} \times \frac{15}{4})B\)

\(\Rightarrow A= \frac{3}{2}B\)

\(\Rightarrow \frac{A}{B} = \frac{3}{2}\)

   \(\Rightarrow\)  A:B = 3:2.

B's share = Rs. \((1210\times\frac{2}{5}) = Rs. 484.\)

Let the third number be x.

Then, first number = 120% of x = \(\frac{120x}{100} = \frac{6x}{5}\)

Second number = 150% of x = \(\frac{150x}{100} = \frac{3x}{2}\)

Therefore Ratio of first two numbers = \(\left(\frac{6x}{5}:\frac{3x}{2}\right)= 12x:15x = 4:5.\)

Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.

Then, 4x - 3x = 1000

x = 1000.

Therefore  B's share = Rs. 2x = Rs. (2 x 1000) = Rs. 2000.

Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively.

Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x)..

\(\Rightarrow(\frac{140}{100}\times5x) , (\frac{150}{100}\times7x) and (\frac{175}{100}\times8x)\)

\(\Rightarrow 7x ,\frac{21x}{2} and 14x.\)

Therefore The required ratio =  \(7x :\frac{21x}{2} :14x.\)

\(\Rightarrow\) 14x : 21x : 28x

  \(\Rightarrow\)2 : 3 : 4.

Quantity of milk = \((60\times\frac{2}{3})litres = 40 litres,\)

Quantity of water in it = (60- 40) litres = 20 litres.

New ratio = 1 : 2

Let quantity of water to be added further be x litres.

Then, milk : water = \((\frac{40}{2+x})\)

Now, \((\frac{40}{2+x}) = \frac{1}{2}\)

\(\Rightarrow\) 20 + x = 80

 \(\Rightarrow\) x = 60.

Therefore Quantity of water to be added = 60 litres.

Originally, let the number of boys and girls in the college be 7x and 8x respectively.

Their increased number is (120% of 7x) and (110% of 8x).

\(\Rightarrow(\frac{120}{100}\times7x) and (\frac{110}{100}\times8x)\)

\(\Rightarrow\frac{42x}{5} and \frac{44x}{5}\)

Therefore The required ratio = \((\frac{42x}{5}:\frac{44x}{5})=21:22.\)

Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively.

Then, \(\frac{2x+4000}{3x+4000} = \frac{40}{57}\)

\(\Rightarrow \) 57(2x + 4000) = 40(3x + 4000)

\(\Rightarrow \) 6x = 68,000

 \(\Rightarrow \)3x = 34,000

Sumit's present salary = (3x + 4000) = Rs.(34000 + 4000) = Rs. 38,000.

(x x 5) = (0.75 x 8)   \(\Rightarrow \) x = \((\frac{6}{5}) = 1.20\)

Let the three parts be A, B, C. Then,

A : B = 2 : 3 and B : C = 5 : 8 =  \((5\times\frac{3}{5}) : (8\times\frac{3}{5}) = 3:\frac{24}{5}
\)

 \(\Rightarrow\)A : B : C = 2 : 3 : \(\frac{24}{5} = 10:15:24\)

\(\Rightarrow\)B =  \((98\times\frac{15}{49}) = 30\)

Given ratio =   \(\frac{1}{2} :\frac{2}{3}:\frac{3}{4}\)     = 6 : 8 : 9.

Therefore 1^st part = Rs. \((782\times\frac{6}{23})\)    = Rs. 204