$$\eqalign{ & {\text{Let Ninad's investment be Rs}}{\text{.}}x \cr & {\text{Then, ratio of capitals}} \cr & = \left( {x \times 12} \right):\left( {2x \times 6} \right):\left( {3x \times 4} \right) \cr & = 12x:12x:12x \cr & = 1:1:1 \cr & \refore {\text{Manav's share}} \cr & = {\text{Rs}}{\text{.}}\left( {45000 \times \frac{1}{3}} \right) \cr & = {\text{Rs}}{\text{.15000}} \cr} $$

P : Q : R
= (25 × 1 + 35 × 2) : (35 × 2 : 25 × 1) : (30 × 3)
= 95 : 95 : 90
= 19 : 19: 18

Let amount invested by Q = q.
$$\eqalign{ & 40000:q = 2:3 \cr & \Rightarrow \frac{{40000}}{q} = \frac{2}{3} \cr & \Rightarrow q = 40000 \times \frac{3}{2} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. 60000}} \cr} $$

$$\eqalign{ & {\text{Ratio of shares}} \cr & = 8:12:14 \cr & = 4:6:7 \cr & \refore {\text{Kiara's share}} \cr & = {\text{Rs}}{\text{.}}\left( {578 \times \frac{7}{{17}}} \right) \cr & = {\text{Rs. }}{\text{238}} \cr} $$

Let initial investment of A is 3x and B is 5x, n C investment is also 5x, but most important to note in this question is time duration of investment
Like, A invested for 12 months, B invested for 12 months and C invested for 6 months.

A : B : C = (3x x 12) : (5x x 12) : (5x x 6)
= 36 : 60 : 30
= 6 : 10 : 5.

? Loss will be divided according to ir investment ratio =

$$\eqalign{ & {\text{Let}}\,{\text{}}\,{\text{total}}\,{\text{profit}}\,{\text{be}}\,Rs.\,Z \cr & {\text{Bharti's}}\,{\text{share}} = {\frac{2}{3}} Z \cr & {\text{Rahul's}}\,{\text{share}} = Z - {\frac{2}{3}} Z \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{Z}{3} \cr & {\text{Rahul:Bharti}} \cr & = \frac{Z}{3}: {\frac{2}{3}} Z = 1:2 \cr & {\text{Now}}\,{\text{let}}\,{\text{}}\,{\text{total}}\,{\text{capital}}\,{\text{be}}\,Rs\,X, \cr & {\text{and}}\,{\text{Bharti}}\,{\text{capital}}\,{\text{was}}\,{\text{used}}\,{\text{for}}\,Y\,{\text{months}}. \cr & {\text{n,}}\,{\text{Rahul}}\,{\text{capital}}\,{\text{will}}\,{\text{be}}\, {\frac{1}{4}} X \cr & {\text{and}}\,{\text{Bharti}}\,{\text{capital}}\,{\text{will}}\,{\text{be}}\,X - {\frac{1}{4}} X \cr & = \frac{{3X}}{4} \cr & \frac{{\frac{1}{4}X*15}}{{\frac{3}{4}X*Y}} = \frac{1}{2} \cr & Y = \frac{{15*2}}{3} = 10 \cr & {\text{So,}}\,{\text{Bharti's}}\,{\text{money}}\,{\text{was}}\,{\text{used}}\,{\text{for}}\,{\text{10}}\,{\text{months}} \cr} $$

$$\eqalign{ & = {\text{Anu}}:{\text{Bimla}} \cr & = 5000:6000 \cr & = 5:6{\text{ }} \cr} $$
Anu's share for managing business
$$\eqalign{ & = 12.5\% {\text{ of Rs}}{\text{.}}\,880 \cr & = {\text{Rs}}{\text{.}}\,110 \cr & {\text{Net profit}} \cr & = {\text{Rs}}{\text{.}}\left( {880 - 110} \right) \cr & = {\text{Rs}}{\text{.}}\,{\text{770}} \cr & {\text{Anu's share}} \cr & = {\text{Rs}}{\text{.}}\left( {770 \times \frac{5}{{11}}} \right) \cr & = {\text{Rs}}{\text{.}}\,{\text{350}} \cr & {\text{Anu's total share}} \cr & = {\text{Rs}}{\text{.}}\left( {110 + 350} \right) \cr & = {\text{Rs}}{\text{.}}\,{\text{460}} \cr & {\text{Bimla's share}} \cr & = {\text{Rs}}{\text{.}}\left( {770 \times \frac{6}{{11}}} \right) \cr & = {\text{Rs}}{\text{.}}\,{\text{420}} \cr} $$

Let Y's investment is used for T months → Now by using formula
$$\eqalign{ & \frac{{5 \times 8}}{{6 \times {{\text{T}}_2}}} = \frac{5}{9} \cr & {\text{T}} = 12{\text{ months}} \cr} $$