\begin{align} & = \sqrt 2 :\left( {1 + \sqrt 3 } \right)::\sqrt {6} : x \cr & \Rightarrow \sqrt {2x} = \sqrt 6 \left( {1 + \sqrt 3 } \right) \cr & \Rightarrow x = \frac{{\sqrt 6 \left( {1 + \sqrt 3 } \right)}}{{\sqrt 2 }} \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, = \sqrt 3 \left( {1 + \sqrt 3 } \right) \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, = \sqrt 3 + 3 \cr\end{align}

Quantity of milk and water in the 36 liter mixture;

27 liter milk and 9 liter water.

Now, 15 liters milk is added then milk becomes 42 liters.

Now, ratio = 42:9 = 14:3.

\begin{align} & {\text{Given}}\, {\text{ratio}} \cr & = \frac{1}{2}:\frac{2}{3}:\frac{3}{4} = 6:8:9. \cr & \therefore {1^{st}}\, {\text{part}} = Rs.\, \left( {782 \times \frac{6}{{23}}} \right) \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, = Rs.\, 204 \cr\end{align}

a : b = 1 : 2

c : d = 1 : 2

e : f = 1 : 2

∴ a = x, b = 2x, c = x, d = 2x, e = x, f = 2x \begin{align} & \therefore \frac{{3 \times x + 5 \times 7 + 7 \times x}}{{3 \times 2x + 5 \times 2x + 7 \times 2x}} \times 1 \cr & \Rightarrow \frac{{15x}}{{30x}} \cr & \Rightarrow \frac{1}{2} \cr\end{align}

Let A's Salary = Rs. 100

Then, B's Salary = Rs. 300

And, C's Salary = Rs 400

Salary has given in 1:3:4 ratio.

Now,

5% increase in A's Salary,

A's new Salary = (100 + 5% of 100) = Rs. 105.

B's Salary increases by 10%, Then,

B's new Salary = (300 + 10% of 200) = Rs. 330.

C's Salary increases by 15%,

C's new Salary = (400 + 15% of 400) = Rs. 460.

Then, ratio of increased Salary,

A:B:C = 105:330:460 = 21:66:92.

Alternative

100(A's salary)===5%↑===> 105(A's increased salary);

300 (B's salary)===10%↑===>330 (B's increased salary);

400 (C's salary)===15%↑===> 460 (C's increased salary).

Ratio of their increased salary = 105:330:480 = 21:66:92