Answer: Option C. -> Rs. 472
Total profit = Rs. 880
Since A gets 15% of total profit for management
∴ Remaining profit
$$\eqalign{
& = 880 - \frac{{880 \times 15}}{{100}} \cr
& = {\text{Rs}}.\,748 \cr} $$
 
A
 
B
Amount
5000
 
6000
Ratio of Capital  
5
  :  
6
The remaining profit is being divided in the ratio of their capital
A's share of profit
$$\eqalign{
& = \frac{{748}}{{\left( {5 + 6} \right)}} \times 5 \cr
& = {\text{Rs}}.\,340 \cr} $$
Total profit received by A
= 340 + 132
= Rs. 472

Answer: Option C. -> Rs. 108
$$\eqalign{
& {\text{Let total profit}} = {\text{16 units }} \cr
& {\text{According to the question,}} \cr
& {\text{Profit share of A}} \cr
& = \frac{3}{{16}} \times 16{\text{ units}} \cr
& = 3{\text{ units}} \cr
& {\text{profit share of B }} \cr
& {\text{ = }}\frac{1}{4} \times 16 = 4{\text{ units}} \cr
& {\text{then profit share of C}} \cr
& = \left[ {16 - \left( {4 + 3} \right)} \right] = 9{\text{ units}} \cr
& {\text{But profit of C}} = {\text{Rs}}{\text{. 243 (given)}} \cr
& {\text{9 units}} = {\text{Rs}}{\text{. 243}} \cr
& {\text{1 unit}} = {\text{Rs}}{\text{. 27}} \cr
& {\text{Profit share of B}} \cr
& = 4{\text{ units}} \cr
& = 27 \times 4 \cr
& = {\text{Rs}}{\text{. 108}} \cr} $$

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

Answer: Option A. -> Rs. 1240
Ratio of initial investments
$$\eqalign{
& = \frac{1}{3}:\frac{1}{4}:\frac{1}{5} \cr
& = 20:15:12 \cr} $$
Let their initial investments be 20x, 15x and 12x respectively
= A : B : C
= (20x × 15 + 10x × 15) : (15x × 30) : (12x × 30)
= 450x : 450x : 360x
= 5 : 5 : 4
$$\eqalign{
& \therefore {\text{C's share}} \cr
& = {\text{Rs}}{\text{.}}\left( {4340 \times \frac{4}{{14}}} \right) \cr
& = {\text{Rs}}{\text{.1240}} \cr} $$

Answer: Option B. -> Rs. 150
$$\eqalign{
& {\text{Let total capital}} = {\text{Rs}}{\text{.}}\,{\text{x}} \cr
& {\text{Then, A's capital}} = {\text{Rs}}{\text{.}}\,\frac{x}{3} \cr} $$
B's capital = (A + C)'s capital ⇒ 2(B's capital)
B's capital = (A + B + C)'s capital = Rs. x
$$\eqalign{
& \Rightarrow {\text{B's capital}} = {\text{Rs}}{\text{.}}\frac{x}{2} \cr
& \Rightarrow {\text{C's capital}} \cr
& = {\text{Rs}}{\text{.}}\left[ {x - \left( {\frac{x}{3} + \frac{x}{2}} \right)} \right] \cr
& = {\text{Rs}}{\text{.}}\,\frac{x}{6} \cr
& \therefore {\text{A}}:{\text{B}}:{\text{C}} \cr
& = \frac{x}{3}:\frac{x}{2}:\frac{x}{6} \cr
& = 2:3:1 \cr
& {\text{So C's share}} \cr
& = {\text{Rs}}{\text{.}}\left( {900 \times \frac{1}{6}} \right) \cr
& = {\text{Rs}}{\text{.}}\,{\text{150}} \cr} $$

Answer: Option D. -> Rs. 6000
 
  A  
  :  
  B  
  :  
  C  
Ratio of Profit →  
  2  
  :  
  3  
  :  
  7  
$$\eqalign{
& {\text{Average gain}} = \frac{{2 + 3 + 7}}{3} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 4{\text{ units}} \cr
& {\text{According to the question,}} \cr
& {\text{4 units}} = {\text{Rs}}{\text{. 8000}} \cr
& {\text{1 unit}} = {\text{Rs}}{\text{. 2000}} \cr
& {\text{3 units}} = 3 \times 2000 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. 6000}} \cr
& \therefore {\text{Share of B}} = {\text{Rs}}{\text{. 6000}} \cr} $$

Answer: Option B. -> 19 : 11 : 10
$$\eqalign{
& {\text{Let the total share}} = {\text{200 units}} \cr
& \therefore {\text{Share of C}} = 200 \times \frac{1}{4} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 50{\text{ units}} \cr
& {\text{Remaining share}} \cr
& = \left( {200 - 50} \right) \cr
& {\text{ = 150 units}} \cr
& \therefore {\text{Share of A}} = \frac{{200}}{{3 + 2}} \times 3 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 120{\text{ units}} \cr
& {\text{Share of B}} = \frac{{200}}{{3 + 2}} \times 2 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 80{\text{ units}} \cr} $$
According to the question,
C received equal amounts from A and B
$$\eqalign{
& \therefore {\text{A's remaining share}} \cr
& = \left( {120 - 25} \right) \cr
& = 95 \cr
& {\text{B's remaining share}} \cr
& = \left( {80 - 25} \right) \cr
& = 55 \cr} $$
 
  A  
  :  
  B  
  :  
  C  
New Ratio →  
  95  
  :  
  55  
  :  
  50  
     
  19  
  :  
  11  
  :  
  10  

Answer: Option D. -> 8 months
$$\eqalign{
& {\text{Suppose B joined for }}x{\text{ months}} \cr
& {\text{Then,}} \cr
& \Rightarrow \frac{{85000 \times 12}}{{42500 \times x}} = \frac{3}{1} \cr
& \Rightarrow x = \frac{{85000 \times 12}}{{42500 \times 3}} \cr
& \Rightarrow x = 8 \cr
& {\text{So, B joined for 8 months}} \cr} $$

Answer: Option D. -> Rs. 28000
Suppose B invested Rs. x for y months
Then, A invested Rs. 3x for 2y months
$$\eqalign{
& {\text{So, A}}:{\text{B}} \cr
& = \left( {3x \times 2y} \right):\left( {x \times y} \right) \cr
& = 6xy:xy \cr
& = 6:1 \cr
& \therefore {\text{B's profit}}:{\text{Total profit}} = 1:7 \cr
& {\text{Let the total profit is Rs}}{\text{. }}x \cr
& {\text{Then,}}\frac{1}{7} = \frac{{4000}}{x} \cr
& \Leftrightarrow x = 28000 \cr} $$

Answer: Option B. -> 3 : 4 : 4
 
  A  
  :  
  B  
  :  
  C  
Capital →  
45000
:
80000
:
120000
Time(year) →
2
 
$$\frac{3}{2}$$
 
1
Profit →
90
:
120
:
120
 
3
:
4
:
4
∴ Required ratio of profit = 3 : 4 : 4