$$\eqalign{ & {\text{Investment of A for 8 months}} \cr & = {\text{Rs}}{\text{.15400}} \cr & {\text{Investment of B for 6 months}} \cr & = {\text{Rs}}{\text{.18200}} \cr & {\text{Investment of C for 8 months}} \cr & = {\text{Rs}}{\text{.12600}} \cr & {\text{Ratio of share of A, B and C}} \cr & = 15400 \times 8:18200 \times 6:12600 \times 8 \cr & = 154 \times 8:182 \times 6:126 \times 8 \cr & = 44:39:36 \cr & {\text{Sum of terms of ratio}} \cr & = 44 + 39 + 36 \cr & = 119 \cr & \refore {\text{ Share of C}} \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{36}}{{119}} \times 28790} \right) \cr & = {\text{Rs}}{\text{.8710}} \approx {\text{Rs}}{\text{.8712}} \cr} $$

A : B : C
(5000 × 4 + 2500 × 8) : (4500 × 6 + 3000 × 6) : (7000 × 6)
= 40000 : 45000 : 42000
= 40 : 45 : 42
$$\eqalign{ & \refore {\text{A's share}} \cr & = {\text{Rs}}{\text{.}}\left( {5080 \times \frac{{40}}{{127}}} \right) \cr & = {\text{Rs}}{\text{.}}\,{\text{1600}} \cr & \refore {\text{B's share}} \cr & = {\text{Rs}}{\text{.}}\left( {5080 \times \frac{{45}}{{127}}} \right) \cr & = {\text{Rs}}{\text{.}}\,{\text{1800}} \cr & \refore {\text{C's share}} \cr & = {\text{Rs}}{\text{.}}\left( {5080 \times \frac{{42}}{{127}}} \right) \cr & = {\text{Rs}}{\text{.}}\,{\text{1680}} \cr} $$

Aman : Rakhi : Sagar
= (70,000 x 36) : (1,05,000 x 30) : (1,40,000 x 24)
= 12 : 15 : 16

Ratio of initial investments
$$\eqalign{ & = {\frac{7}{2}:\frac{4}{3}:\frac{6}{5}} \cr & = 105:40:36 \cr} $$
Let initial investments be 105x, 40x and 36x
$$\left( {105x \times 4 + \frac{{150}}{{100}} \times 105x \times 8} \right)$$      $$:$$ $$\left( {40x \times 12} \right)$$   $$:$$ $$\left( {36x \times 12} \right)$$
$$\eqalign{ & = 1680x:480x:432x \cr & = 35:10:9 \cr & {\text{Hence,}}{\kern 1pt} {\text{B's}}{\kern 1pt} {\text{share}} \cr & = {\text{Rs}}{\text{.}}\left( {21600 \times \frac{{10}}{{54}}} \right) \cr & = {\text{Rs}}{\text{.}}\,4000 \cr} $$

A : B : C
= (25 lakhs × 1 + 35 lakhs × 2) : (35 lakhs × 2 + 25 lakhs × 1) : (30 lakhs × 3)
= 95 lakhs : 95 lakhs : 90 lakhs
= 19 : 19 : 18

Suppose,
Swati invested Rs. 5x for 7 months
And
Rajni invested Rs. 6x for y months
Then,
$$\eqalign{ & \Rightarrow \frac{{5x \times 7}}{{6x \times y}} = \frac{5}{9} \cr & \Rightarrow 30y = 315 \cr & \Rightarrow y = 10\frac{1}{2} \cr} $$
Hence, Rajni's capital was used for $${\text{10}}\frac{1}{2}$$ months

Sonia : Vivek : Sagar
= (60000 × 24) : (140000 × 18) : (120000 × 12)
= 1440000 : 2520000 : 1440000
= 4 : 7 : 4
$$\eqalign{ & \refore {\text{Vivek's share}} \cr & \Rightarrow {\text{Rs}}{\text{.}}\,\left( {450000 \times \frac{7}{{15}}} \right) \cr & \Rightarrow {\text{Rs}}{\text{. 210000}} \cr} $$

Lert share of A = Rs. x
According to question,
$$\eqalign{ & {\text{A}}:{\text{B}}:{\text{C}} \cr & {\text{Capital}} \to x:2x:\left( {4x - 50} \right) \cr & \Rightarrow \left( {x + 2x + 4x - 50} \right) = 13950 \cr & \Rightarrow 7x - 50 = 13950 \cr & \Rightarrow 7x = 14000 \cr & \Rightarrow x = 2000 \cr & {\text{Share of A}} = {\text{Rs}}{\text{. 2000}} \cr} $$