Partnership

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

$${\text{Subhas}}:{\text{Ishanta}}$$
$$ = \left( {25000 \times 36} \right):\left( {15000 \times 6 + 30000 \times 24} \right)$$
$$ = 900000:810000$$
$$ = 10:9$$
$$\therefore {\text{Ishanta's share}}$$
$$ ⇒ {\text{₹}}{\text{.}}\left( {247000 \times \frac{9}{{19}}} \right)$$
$$ ⇒ {\text{₹}}{\text{.117000}}$$

$${\text{Here}}\,{{\text{p}}_1}:{{\text{p}}_2}:{{\text{p}}_3} = 5:3:12$$
$${\text{and}}\,{{\text{x}}_1}:{{\text{x}}_2}:{{\text{x}}_3} = 5:6:8$$
$${\text{According}}\,{\text{to}}\,{\text{the}}\,{\text{formula}}$$
$${\text{Required}}\,{\text{ratio}}$$
$$ = \frac{{{{\text{p}}_1}}}{{{{\text{x}}_1}}}:\frac{{{{\text{p}}_2}}}{{{{\text{x}}_2}}}:\frac{{{{\text{p}}_3}}}{{{{\text{x}}_3}}}$$
$$ = \frac{5}{5}:\frac{3}{6}:\frac{{12}}{8}$$
$$ = 1:\frac{1}{2}:\frac{3}{2}$$
$$ = 2:1:3$$
$$$$
$${\bf{Alternate:}}$$
$${\text{Profit}} = {\text{Time}} \times {\text{Capital invested}}$$
$${\text{Time}} = \frac{{{\text{Profit}}}}{{{\text{Capital invested}}}}$$
$${\text{Required ratio of time}}$$
$$ = \frac{5}{6}:\frac{3}{6}:\frac{{12}}{8}$$
$$ = 1:\frac{1}{2}:\frac{3}{2}$$
$$ = 2:1:3$$

Given
X : Z = 2 : 1
X : Y = 3 : 2
X : Z = 2 : 1 (multiply with 3)
X : Y = 3 : 2 (multiply with 2)
i.e X : Z = 6 : 3
X : Y = 6 : 4
∴ X : Y : Z = 6 : 4 : 3
we know that
(6 + 4 + 3) unit's = ₹157300
13 unit's = ₹157300
1 unit = ₹12100
4 unit's = ₹12100 × 4 = ₹ 48400
∴ Share of Y = ₹ 48400

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

$${\text{Abdul}}:{\text{Madhu}}$$
$$ = \left( {38000 \times 12} \right):\left( {55000 \times 7} \right)$$
$$ = 456000:385000$$
$$ = 456:385$$
$$\therefore {\text{Required difference}}$$
$$ = {\text{₹}}{\text{.}}\,\left[ {22000 \times \left( {\frac{{456}}{{841}} - \frac{{385}}{{841}}} \right)} \right]$$
$$ = {\text{₹}}{\text{.}}\left( {22000 \times \frac{{71}}{{841}}} \right)$$
$$ = {\text{₹ }}{\text{1857}}{\text{.31}}$$
$$ = {\text{₹ }}{\text{1857 }}$$

$${\text{Gautam}}:{\text{Jatin}}$$
$$ = \left( {6000 \times 12} \right):\left( {35000 \times 8} \right)$$
$$ = 720000:280000$$
$$ = 18:7$$

$${\text{Fatima}}:{\text{Arjun}}$$
$$ = \left( {50000 \times 36} \right):\left( {80000 \times 30} \right)$$
$$ = 1800000:2400000$$
$$ = 3:4$$
$$\therefore \,{\text{Fatima's share}}$$
$$ = {\text{₹}}{\text{.}}\left( {24500 \times \frac{3}{7}} \right)$$
$$ = {\text{₹ }}{\text{10500 }}$$

$${\text{Pratap}}:{\text{Ram}}:{\text{Harshad}}$$
$$ = 2700:8100:7200$$
$$ = 3:9:8$$
$${\text{Let the total profit be ₹}}.\,x$$
$${\text{Then, Ram's share}}$$
$$ = {\text{₹}}{\text{.}}\,\left( {\frac{9}{{20}}x} \right)$$
$$\therefore \frac{9}{{20}}x = 3600$$
$$ ⇒ x = \left( {\frac{{3600 \times 20}}{9}} \right)$$
$$ ⇒ x = 8000$$
$${\text{Hence,}}$$
$${\text{Total profit}} = {\text{₹}}{\text{. 8000}}$$

Chandan : Rani : Joydeep
= (70000 × 36) : (105000 × 30) : (140000 × 24)
= 12 : 15 : 16