Partnership - 04

Explanation:-

Let A's capital = Rs. x
Then, B's capital = Rs. (x - 600)
C's capital = Rs. (x - 600) - 300 = Rs. (x - 900)
∴ x + (x - 600) + (x - 900) = 3000
⇒ 3x = 45000
⇒ x = 1500
$$\eqalign{ & {\text{So, A}}:{\text{B}}:{\text{C}} \cr & = 1500:900:600 \cr & = 5:3:2 \cr & {\text{Hence, B's share}} \cr & = {\text{Rs}}{\text{.}}\left( {886 \times \frac{3}{{10}}} \right) \cr & = {\text{Rs}}{\text{. 265}}{\text{.80}} \cr}$$

Explanation:-

$$\eqalign{ & {\text{Ratio of shares}} \cr & = 1500:2500 \cr & = 3:5 \cr & {\text{Share of first friend}} \cr & = {\text{Rs}}{\text{.}}\left[ {\frac{{400}}{2} + \left( {400 \times \frac{3}{8}} \right)} \right] \cr & = {\text{Rs}}.\left( {200 + 150} \right) \cr & = {\text{Rs}}{\text{.350}} \cr & {\text{Share of second friend}} \cr & = {\text{Rs}}{\text{.}}\left[ {\frac{{400}}{2} + \left( {400 \times \frac{5}{8}} \right)} \right] \cr & = {\text{Rs}}.\left( {200 + 250} \right) \cr & = {\text{Rs}}{\text{.450}} \cr}$$

Explanation:-

$$\eqalign{ & \because {\text{Ratio of shares}} \cr & = 11:16.5:8.25 \cr & = 4:6:3 \cr & {\text{Anil's share}} \cr & = {\text{Rs}}{\text{.}}\left( {19.5 \times \frac{3}{{13}}} \right) \cr & = {\text{Rs. }}{\text{4}}{\text{.5 lakh}} \cr & \therefore {\text{Required amount}} \cr & = 50\% {\text{ of 4}}{\text{.5 lakh}} \cr & = {\text{Rs. }}{\text{2}}{\text{.25 lakh}} \cr}$$

Explanation:-

Let the total profit = Rs. k
According to the question,
Remaining profit after paying 20% working
Partner's commission = (k - 8000)
$$\eqalign{ & \therefore \,\left( {k - 8000} \right) \times \frac{{20}}{{100}} = 8000 \cr & \Leftrightarrow k = 48000 \cr & \therefore {\text{ Total profit}} = {\text{Rs}}{\text{. 48000}} \cr}$$

Explanation:-

$$\eqalign{ & \because {\text{P}}:{\text{Q}}:{\text{R}} \cr & = 45000:70000:90000 \cr & = 9:14:18 \cr & \therefore \,{\text{Q's share}} \cr & = {\text{Rs}}{\text{.}}\left( {164000 \times \frac{{14}}{{41}}} \right) \cr & = {\text{Rs. }}{\text{56000}} \cr}$$

Explanation:-

$$\eqalign{ & {\text{Ratio of shares}} \cr & = 8:12:14 \cr & = 4:6:7 \cr & \therefore {\text{Kiara's share}} \cr & = {\text{Rs}}{\text{.}}\left( {578 \times \frac{7}{{17}}} \right) \cr & = {\text{Rs. }}{\text{238}} \cr}$$

Explanation:-

Let total capital be Rs. x
$$\eqalign{ & {\text{Then,}} \cr & {\text{Rahul's share}} \cr & = {\text{Rs}}{\text{.}}\frac{x}{2} \cr & {\text{Arun's share}} = {\text{Rs}}{\text{.}}\frac{x}{3} \cr & {\text{Sumit's share}} \cr & = {\text{Rs}}{\text{.}}\left[ {x - \left( {\frac{x}{2} + \frac{x}{3}} \right)} \right] \cr & = {\text{Rs}}{\text{. }}\frac{x}{6} \cr & \therefore {\text{Required ratio}} \cr & = \frac{x}{2}:\frac{x}{3}:\frac{x}{6} \cr & = \frac{1}{2}:\frac{1}{3}:\frac{1}{6} \cr & = 3:2:1 \cr}$$

Explanation:-

In this type of question as time frame for both investors is equal then just get the ratio of their investments.
P : Q = 85000 : 15000
= 85 : 15
= 17 : 3

Explanation:-

$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{total}}\,{\text{profit}}\,{\text{be}}\,Rs.\,Z \cr & {\text{Bharti's}}\,{\text{share}} = \left( {\frac{2}{3}} \right)Z \cr & {\text{Rahul's}}\,{\text{share}} = Z - \left( {\frac{2}{3}} \right)Z \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{Z}{3} \cr & {\text{Rahul:Bharti}} \cr & = \frac{Z}{3}:\left( {\frac{2}{3}} \right)Z = 1:2 \cr & {\text{Now}}\,{\text{let}}\,{\text{the}}\,{\text{total}}\,{\text{capital}}\,{\text{be}}\,Rs\,X, \cr & {\text{and}}\,{\text{Bharti}}\,{\text{capital}}\,{\text{was}}\,{\text{used}}\,{\text{for}}\,Y\,{\text{months}}. \cr & {\text{then,}}\,{\text{Rahul}}\,{\text{capital}}\,{\text{will}}\,{\text{be}}\,\left( {\frac{1}{4}} \right)X \cr & {\text{and}}\,{\text{Bharti}}\,{\text{capital}}\,{\text{will}}\,{\text{be}}\,X - \left( {\frac{1}{4}} \right)X \cr & = \frac{{3X}}{4} \cr & \frac{{\frac{1}{4}X*15}}{{\frac{3}{4}X*Y}} = \frac{1}{2} \cr & Y = \frac{{15*2}}{3} = 10 \cr & {\text{So,}}\,{\text{Bharti's}}\,{\text{money}}\,{\text{was}}\,{\text{used}}\,{\text{for}}\,{\text{10}}\,{\text{months}} \cr}$$

Explanation:-

Just take care of the months of investment, rest all will be simple.

Yogesh : Pranab : Atul
= 45000 × 12 : 60000 × 9 : 90000 × 3
= 2 : 2 : 1

Atul's share
$$\eqalign{ & = {\text{Rs}}{\text{. }}20000 \times \frac{1}{5} \cr & = {\text{Rs}}{\text{. }}4000 \cr}$$