Partnership

$$A:B:C$$
$$ = \left( {10 \times 7} \right):\left( {12 \times 5} \right):\left( {15 \times 3} \right)$$
$$ = 70:60:45$$
$$ = 14:12:9$$
$$\therefore {\text{C's rent}} = {\text{₹}}{\text{.}}\left( {175 \times \frac{9}{{35}}} \right)$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{₹}}{\text{. }}45$$

Assume that investment of C = x
Then, investment of A = 2x
Investment of B = $$\frac{{2{\text{A}}}}{3}$$ = $$\frac{{4{\text{x}}}}{3}$$ (since ratio of investment of A : B = 2 : 3 i.e B = $$\frac{{2{\text{A}}}}{3}$$)
A : B : C
= 2x : $$\frac{{4{\text{x}}}}{3}$$ : x
= 2 : $$\frac{4}{3}$$ : 1
= 6 : 4 : 3
$${\text{B's Share}}$$
$$ = 157300 \times \frac{4}{{6 + 4 + 3}}$$
$$ = 157300 \times \frac{4}{{13}}$$
$$ = 12100 \times 4$$
$$ = {\text{₹}}{\text{. 48400}}$$

A : B : C
= (20,000 × 24) : (15,000 × 24) : (20,000 × 18)
= 4 : 3 : 3.
$${\text{So B's Share}}$$
$$ = {\text{₹}}{\text{. }}25000 \times \frac{3}{{10}}$$
$$ = {\text{₹}}{\text{. 7500}}$$

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

Let C = x.
Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000
So,×= x + 5000 = x + 9000 = 50000
⇒ 3x = 36000
⇒×= 12000
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12
$${\text{So A's Share}}$$
$$ = {\text{₹}}{\text{. 3}}5000 \times \frac{{21}}{{50}}$$
$$ = {\text{₹}}{\text{. 14700}}$$

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