Answer: Option B. -> 3:4

They should share the profits in the ratio of their investments.
The ratio of the investments made by A and B =
6000 : 8000 => 3:4

Answer: Option B. -> Either III only, or I and II together

I and II give, profit after 3 years = Rs.

3
x 22000

= Rs. 8250.
8

From III also, profit after 3 years = Rs. (2750 x 3) = Rs. 8250.

P's share = Rs.

8250 x
5

= Rs. 3750.
11

Thus, (either III is redundant [or] I and II are redundant).

Correct answer is (B).

Answer: Option A. -> $ 2000 million
Fraction of profit received by each one of Jhon and Mona
$$\eqalign{
& = \frac{{\left( {1 - \frac{2}{3}} \right)}}{2} \cr
& = \frac{1}{6} \cr} $$
Ratio of capitals of Jhon, Mona and Gordon = Ratio of their profits
$$\eqalign{
& \frac{1}{6}:\frac{1}{6}:\frac{2}{3} = 1:1:4 \cr
& {\text{Let the total capital be Rs}}{\text{.}}x \cr
& {\text{Then,}} \cr
& \frac{1}{6}{\text{of }}\left( {7\% {\text{ of }}x - 4\% {\text{ of }}x} \right) \cr
& = \$ {\text{ 60 million}} \cr
& \Rightarrow 3\% \,{\text{of }}x = \$ {\text{ }}3{\text{60 million}} \cr
& \Rightarrow x = \$ \left( {\frac{{360 \times 100}}{3}} \right){\text{million}} \cr
& \Rightarrow x = \$ {\text{ 12000 million }} \cr
& \therefore {\text{ Mona's capital }} \cr
& {\text{ = }}\left( {\frac{1}{6} \times \$ {\text{12000 million }}} \right) \cr
& = \$ \,200{\text{0 million }} \cr} $$

Answer: Option B. -> Rs. 39375
$$\eqalign{
& {\text{Let the total profit be Rs}}{\text{. }}x \cr
& {\text{Then, }}60\% {\text{ of the profit}} \cr
& = {\text{Rs}}{\text{.}}\left( {\frac{{60}}{{100}} \times x} \right) \cr
& = {\text{Rs}}{\text{.}}\,\frac{{3x}}{5} \cr} $$
From this part of the profit each gets = $${\text{Rs}}{\text{.}}\,\frac{{3x}}{{10}}$$
$$\eqalign{
& 40\% {\text{ of total profit }} \cr
& = {\text{Rs}}{\text{.}}\left( {\frac{{40}}{{100}} \times x} \right) \cr
& = {\text{Rs}}{\text{.}}\,\frac{{2x}}{5} \cr} $$
Now, this amount of Rs. $$\frac{2x}{5}$$ has been divided in the ratio of capitals, which is
125000 : 85000 or 25 : 17 as interests
∴ Interest on first capital
$$\eqalign{
& = {\text{ Rs}}{\text{.}}\left( {\frac{{2x}}{5} \times \frac{{25}}{{42}}} \right) \cr
& {\text{ = Rs}}{\text{.}}\,\frac{{5x}}{{21}} \cr} $$
Interest on second capital
$$\eqalign{
& = {\text{Rs}}{\text{.}}\left( {\frac{{2x}}{5} \times \frac{{17}}{{42}}} \right) \cr
& {\text{ = Rs}}{\text{.}}\,\frac{{17x}}{{105}} \cr} $$
Total money received by first partner
$$\eqalign{
& = {\text{Rs}}{\text{.}}\left( {\frac{{3x}}{{10}} + \frac{{5x}}{{21}}} \right) \cr
& {\text{ = Rs}}{\text{.}}\,\frac{{113x}}{{210}}{\text{ }} \cr} $$
Total money received by second partner
$$\eqalign{
& = {\text{Rs}}{\text{.}}\left( {\frac{{3x}}{{10}} + \frac{{17x}}{{105}}} \right) \cr
& {\text{ = Rs}}{\text{.}}\,\frac{{97x}}{{210}} \cr
& \therefore \frac{{113x}}{{210}} - \frac{{97x}}{{210}} = 3000 \cr
& \Rightarrow x = 39375{\text{ }} \cr
& {\text{Hence,}} \cr
& {\text{Total profit Rs}}{\text{. 39375}} \cr} $$

Answer: Option D. -> 11 months
Let capital of X be Rs. 11x and Y's capital be Rs. 12x
and let time for which Y invested capital is T2 months
by using formula,
$$\eqalign{
& \Leftrightarrow \frac{{{{\text{C}}_1} \times {{\text{T}}_1}}}{{{{\text{C}}_2} \times {{\text{T}}_2}}} = \frac{{{{\text{P}}_1}}}{{{{\text{P}}_2}}} \cr
& \Leftrightarrow \frac{{11x \times 8}}{{12x \times {{\text{T}}_2}}} = \frac{2}{3} \cr
& \Leftrightarrow {{\text{T}}_2} = 11{\text{ months}} \cr} $$
Hence the time for which Y invested his capital is 11 months

Answer: Option C. -> Rs. 460, Rs. 420
$$\eqalign{
& = {\text{Anu}}:{\text{Bimla}} \cr
& = 5000:6000 \cr
& = 5:6{\text{ }} \cr} $$
Anu's share for managing business
$$\eqalign{
& = 12.5\% {\text{ of Rs}}{\text{.}}\,880 \cr
& = {\text{Rs}}{\text{.}}\,110 \cr
& {\text{Net profit}} \cr
& = {\text{Rs}}{\text{.}}\left( {880 - 110} \right) \cr
& = {\text{Rs}}{\text{.}}\,{\text{770}} \cr
& {\text{Anu's share}} \cr
& = {\text{Rs}}{\text{.}}\left( {770 \times \frac{5}{{11}}} \right) \cr
& = {\text{Rs}}{\text{.}}\,{\text{350}} \cr
& {\text{Anu's total share}} \cr
& = {\text{Rs}}{\text{.}}\left( {110 + 350} \right) \cr
& = {\text{Rs}}{\text{.}}\,{\text{460}} \cr
& {\text{Bimla's share}} \cr
& = {\text{Rs}}{\text{.}}\left( {770 \times \frac{6}{{11}}} \right) \cr
& = {\text{Rs}}{\text{.}}\,{\text{420}} \cr} $$

Answer: Option A. -> 3 : 4
Let A's capital = Rs. x
Let B's capital = Rs. y
Now, according to the question,
 
A
B
Capital →  
x
y
Time (in month) →  
(9 + 1) = 10  
9
Ratio of profit →  
5
6
$$\eqalign{
& {\text{We know,}} \cr
& \frac{{10 \times x}}{{x \times y}} = \frac{5}{6} \cr
& \Leftrightarrow \frac{x}{y} = \frac{3}{4} \cr} $$
Hence the required ratio of capital of A and B is = 3 : 4

Answer: Option B. -> Rs. 320
∵ Loss will be divided according to their investment ratio =
A  
  :  
  B
3000
:
2400
5
:
4
$$\eqalign{
& {\text{Loss of B}} = \frac{4}{{\left( {5 + 4} \right)}} \times 720 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. 320}} \cr} $$

Answer: Option D. -> 8 : 6 : 3
$$\eqalign{
& {\text{3A}} = {\text{4B}} \cr
& {\text{B}} = {\text{2C}} \cr
& \frac{{\text{A}}}{{\text{B}}} = \frac{4}{3} \cr
& \frac{{\text{B}}}{{\text{C}}} = \frac{2}{1} \cr
& {\text{A}}\,\,\,\,\,\,\,\,{\text{B}}\,\,\,\,\,\,\,\,{\text{C}} \cr
& {\text{4}}\,\,\,\,\,\,\,\,\,\,{\text{3}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,{\text{2}}\,\,\,\,\,\,\,\,\,\,{\text{1}} \cr
& \boxed{{\text{8}}\,\,:\,\,6\,\,\,:\,\,\,3\,} \cr} $$

Answer: Option C. -> Rs. 15000
$$\eqalign{
& {\text{Let Ninad's investment be Rs}}{\text{.}}x \cr
& {\text{Then, ratio of capitals}} \cr
& = \left( {x \times 12} \right):\left( {2x \times 6} \right):\left( {3x \times 4} \right) \cr
& = 12x:12x:12x \cr
& = 1:1:1 \cr
& \therefore {\text{Manav's share}} \cr
& = {\text{Rs}}{\text{.}}\left( {45000 \times \frac{1}{3}} \right) \cr
& = {\text{Rs}}{\text{.15000}} \cr} $$