$$\eqalign{ & {\text{Let}}\,{\text{}}\,{\text{total}}\,{\text{profit}}\,{\text{be}}\,{\text{Rs}}{\text{.}}\,{\text{100}} \cr & {\text{After}}\,{\text{paying}}\,{\text{to}}\,{\text{charity,}}\,{\text{A's}}\,{\text{share}} \cr & = Rs.\,\left( {95 \times \frac{3}{5}} \right) = Rs.\,57 \cr & {\text{If}}\,{\text{A's}}\,{\text{share}}\,{\text{is}}\,Rs.\,57, \cr & {\text{Total}}\,{\text{profit}} = Rs.\,100 \cr & {\text{If}}\,{\text{A's}}\,{\text{share}}\,Rs.\,855, \cr & {\text{Total}}\,{\text{profit}} \cr & = {\frac{{100}}{{57}} \times 855} \cr & = 1500 \cr} $$

$$\eqalign{ & {\text{Simran}}\,{\text{:}}\,{\text{Nanda}} \cr & = \left( {50000 \times 36} \right):\left( {80000 \times 30} \right) \cr & = 3:4 \cr & \refore {\text{Simran's}}\,{\text{share}} \cr & = Rs.\,\left( {24500 \times \frac{3}{7}} \right) \cr & = Rs.\,10,500 \cr} $$

Let money invested by A, B and C be Rs. x, Rs. 2x and Rs. 3x respectively
Then, A : B : C
$$\eqalign{ & = \left( {x \times 12} \right):\left( {2x \times 6} \right):\left( {3x \times 4} \right) \cr & = 12x:12x:12x \cr & = 1:1:1 \cr & \refore {\text{C's share}} \cr & = {\text{Rs}}{\text{.}}\left( {27000 \times \frac{1}{3}} \right) \cr & = {\text{Rs. }}{\text{9000}} \cr} $$

Suppose Ramesh invested Rs. x. Then,
Manoj : Ramesh = 120000 × 6 : x × 12.
$$\eqalign{ & \frac{{720000}}{{12{\text{x}}}}:\frac{{6000}}{{3000}} \cr & \Rightarrow {\text{x}} = \frac{{720000}}{{24}} \cr & \Rightarrow {\text{x}} = 30000 \cr} $$

$$\eqalign{ & = {\text{A}}:{\text{B}}:{\text{C}}:{\text{D}} \cr & = 15 \times 4:12 \times 2:18 \times 6:16 \times 5 \cr & = 60:24:108:80 \cr & = 15:6:27:20 \cr & {\text{Let total rent be Rs}}{\text{.}}x \cr & {\text{Then,}} \cr & {\text{A's share}} = {\text{Rs}}{\text{.}}\left( {\frac{{15x}}{{68}}} \right) \cr & \refore \,\frac{{15x}}{{68}} = 1020 \cr & \Rightarrow x = \left( {\frac{{1020 \times 68}}{{15}}} \right) \cr & \Rightarrow x = 4624 \cr & {\text{Hence, C's share}} \cr & = {\text{Rs}}{\text{.}}\left( {4624 \times \frac{{27}}{{68}}} \right) \cr & = {\text{Rs}}{\text{.}}\,{\text{1836}} \cr} $$

$$\eqalign{ & \because {\text{P}}:{\text{Q}}:{\text{R}} \cr & = 45000:70000:90000 \cr & = 9:14:18 \cr & \refore \,{\text{Q's share}} \cr & = {\text{Rs}}{\text{.}}\left( {164000 \times \frac{{14}}{{41}}} \right) \cr & = {\text{Rs. }}{\text{56000}} \cr} $$

Let initial investments of A, B and C be Rs. 5x, Rs. 6x and Rs. 8x respectively
Then, A : B : C
[5x × 12 + (160% of 5x) × 12] : (6x × 24) : (8x × 12 + 4x × 12)
= 156x : 144x : 144x
= 13 : 12 : 12

$$\eqalign{ & {\text{3A}} = {\text{4B}} \cr & {\text{B}} = {\text{2C}} \cr & \frac{{\text{A}}}{{\text{B}}} = \frac{4}{3} \cr & \frac{{\text{B}}}{{\text{C}}} = \frac{2}{1} \cr & {\text{A}}\,\,\,\,\,\,\,\,{\text{B}}\,\,\,\,\,\,\,\,{\text{C}} \cr & {\text{4}}\,\,\,\,\,\,\,\,\,\,{\text{3}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,{\text{2}}\,\,\,\,\,\,\,\,\,\,{\text{1}} \cr & \boxed{{\text{8}}\,\,:\,\,6\,\,\,:\,\,\,3\,} \cr} $$