Partnership

Let C subscribes the business = ₹ x
A : B : C
Capital → (x + 12000) : (x + 5000) : x
Note: Profit would be divide in the ratio of their capitals
we know that,
$$ ⇒ \left( {x + 12000} \right) + \left( {x + 5000} \right) +×= 47000$$
$$ ⇒ 3x + 17000 = 47000$$
$$ ⇒ 3x = 30000$$
$$ ⇒ x = 10000$$
$${\text{ A }}:{\text{ B }}:{\text{ C}}$$
$${\text{Capital}} \to 22000:15000:10000$$
$${\text{Profit}} \to {\text{ }}22{\text{ }}:{\text{ }}15{\text{ }}:{\text{ }}10$$
$$\left( {22 + 15 + 10} \right){\text{ unit's}} = {\text{4700}}$$
$${\text{1 unit}} = \frac{{4700}}{{47}} = 100$$
$${\text{Share of C}} = 10{\text{ unit's}} = 10 \times 100 = {\text{₹}}.1000$$
$$$$

= (60000 × 24) : (140000 × 18) : (120000 × 12)
= 1440000 : 2520000 : 1440000
= 4 : 7 : 4
$$\therefore {\text{Vivek's share}}$$
$$ ⇒ {\text{₹}}{\text{.}}\,\left( {450000 \times \frac{7}{{15}}} \right)$$
$$ ⇒ {\text{₹}}{\text{. 210000}}$$

Let the initial capital of P and Q be ₹ 2x and ₹ 3x respectively
Then, ratio of profit's
$$ = \left( {2x \times 12} \right):\left( {3x \times 24} \right)$$
$$ = 24x:72x$$
$$ = 1:3$$
$$\therefore {\text{Q's share}}$$
$$ = {\text{₹}}{\text{.}}\left( {26000 \times \frac{3}{4}} \right)$$
$$ = {\text{₹ }}{\text{19500}}$$

Let C subscribes the business = ₹ x
A : B : C
Capital → (x + 12000) : (x + 5000) : x
Note: Profit would be divide in the ratio of their capitals
we know that,
$$ ⇒ \left( {x + 12000} \right) + \left( {x + 5000} \right) +×= 47000$$
$$ ⇒ 3x + 17000 = 47000$$
$$ ⇒ 3x = 30000$$
$$ ⇒ x = 10000$$
$${\text{ A }}:{\text{ B }}:{\text{ C}}$$
$${\text{Capital}} \to 22000:15000:10000$$
$${\text{Profit}} \to {\text{ }}22{\text{ }}:{\text{ }}15{\text{ }}:{\text{ }}10$$
$$\left( {22 + 15 + 10} \right){\text{ unit's}} = {\text{4700}}$$
$${\text{1 unit}} = \frac{{4700}}{{47}} = 100$$
$${\text{Share of C}} = 10{\text{ unit's}} = 10 \times 100 = {\text{₹}}.1000$$
$$$$

Akhilesh : Vivek : Joydeep
= (60000 × 24) : (140000 × 18) : (120000 × 12)
= 1440000 : 2520000 : 1440000
= 4 : 7 : 4
$$\therefore {\text{Vivek's share}}$$
$$ ⇒ {\text{₹}}{\text{.}}\,\left( {450000 \times \frac{7}{{15}}} \right)$$
$$ ⇒ {\text{₹}}{\text{. 210000}}$$

Let the initial capital of P and Q be ₹ 2x and ₹ 3x respectively
Then, ratio of profit's
$$ = \left( {2x \times 12} \right):\left( {3x \times 24} \right)$$
$$ = 24x:72x$$
$$ = 1:3$$
$$\therefore {\text{Q's share}}$$
$$ = {\text{₹}}{\text{.}}\left( {26000 \times \frac{3}{4}} \right)$$
$$ = {\text{₹ }}{\text{19500}}$$