Here capital is not the same.
Suresh invested 20000 for initial 6 months and 15000 for the next 6 months. Hence his term of ratio
$=(20000×6+15000×6)$
Kiran invested Rs.30000 for 4 months and Rs.50000 for next 4 months. Hence his term of ratio
$=(30000×4+50000×4)$
Suresh : Kiran
$=\left(20000\times6+15000\times6\right)$$:\left(30000\times4+50000\times4\right)$
$=\left(20\times6+15\times6\right)$:$\left(30\times4+50\times4\right)$=$\left(20\times3+15\times3\right)$:$\left(30\times2:50\times2\right)$=105:160=21:32
Suppose B was there in the business for $x$ months. Then
A : B $=76000×12:57000×x$
Therefore,
$76000×12:57000×x=2:1$
$76×12:57x=2:1$
$76×12×1=57x×2$
$76×4=19x×2$
$4×4=x×2$
$x=8$
Hence B was there in the business for 8 months, or joined after 12-8 = 4 months
Ratio of the profits of Kamal and Kiran
$=25000×12:60000×8=25×12:60×8 =5×3:12×2=5:4×2=5:8$
Let the total profit $=x$
Then Kamal received $\dfrac{10x}{100}=\dfrac{x}{10}$ as commission for managing the business.
Remaining profit $=x-\dfrac{x}{10}=\dfrac{9x}{10}$ which is shared in the ratio $5:8$
Total amount received by Kamal $=\dfrac{x}{10}+\dfrac{9x}{10}×\dfrac{5}{13}$
$\Rightarrow \dfrac{x}{10}+\dfrac{9x}{10}×\dfrac{5}{13}=58000$
$ \Rightarrow x + 9x×\dfrac{5}{13}=580000$
$ \Rightarrow x\left(1+\dfrac{45}{13}\right)=580000$
$\Rightarrow x×\dfrac{58}{13}=580000$
$\Rightarrow x×\dfrac{1}{13}=10000$
$ \Rightarrow x=130000$
Kirans share = $130000-58000=72000$
Ratio of initial investments =$ \left(\dfrac{7}{2} :\dfrac{4}{3} :\dfrac{6}{5} \right) $= 105 : 40 : 36.
Let the initial investments be 105$ x $, 40$ x $ and 36$ x $.
$\therefore$ A : B : C =$ \left(105x \times 4 +\dfrac{150}{100} \times 105x \times 8\right) $: $\left(40 x \times 12\right)$ :$ \left(36 x \times 12\right)$
= 1680$ x $ : 480$ x $ : 432$ x $ = 35 : 10 : 9.
Hence, Bs share = Rs.$ \left(21600 \times\dfrac{10}{54} \right) $= Rs. 4000.
A : B : C = $\left(20,000 \times 24\right)$ :$\left (15,000 \times 24\right)$ : $\left(20,000 \times 18\right)$ = 4 : 3 : 3.
$\therefore$ Bs share = Rs.$ \left(25000 \times\dfrac{3}{10} \right) $= Rs. 7,500.
For managing, A received = 5% of Rs. 7400 = Rs. 370.
Balance = Rs. $\left(7400 - 370\right)$ = Rs. 7030.
Ratio of their investments = $\left(6500 \times 6\right)$ : $\left(8400 \times 5\right)$ : $\left(10000 \times 3\right)$
= 39000 : 42000 : 30000
= 13 : 14 : 10
$\therefore$ Bs share = Rs.$ \left(7030 \times\dfrac{14}{37} \right) $= Rs. 2660.
P : Q : R = $120000:135000:150000$
$=120:135:150=24:27:30=8:9:10$
Share of P
$=56700×\dfrac{8}{27}=2100×8=16800$
Share of Q
$=56700×\dfrac{9}{27}=2100×9= 18900$
Share of R
$=56700×\dfrac{10}{27}=2100×10=21000$
Assume that investment of C $=x$
Then, investment of A $=2x$
Investment of B $=\dfrac{4x}{3}$
A:B:C $=2x:\dfrac{4x}{3}:x$
=2:$\dfrac{4}{3}$:1=6:4:3
Bs share $=157300×\dfrac{4}{6+4+3}$
$=157300×\dfrac{4}{13}=12100×4=48400$
A : B : C
=$\left(20000\times5+15000×7\right)$:$\left(20000\times5+16000\times7\right)$:$\left(20000\times 5+26000\times 7\right)$
=$\left (20\times 5 + 15\times 7\right)$: $\left (20\times 5 + 16\times 7\right)$: $\left (20\times 5 + 26\times 7\right)$
$= 205 : 212 : 282$
As share $=69900×\dfrac{205}{205+212+282}$
$=69900×\dfrac{205}{699}=20500$
Suppose Cs capital $=x$. Then,
Bs capital $=4x$ [Since Bs capital is four times Cs capital]
As capital $=6x$ [Since twice As capital is equal to thrice Bs capital]
A : B : C $=6x:4x:x$
$= 6 : 4 : 1$
Bs share
=$16500×\dfrac{4}{11}$=$1500×4=6000$