Partnership - Aptitude MCQ Questions and Solutions with Explanations

$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{total}}\,{\text{profit}}\,{\text{be}}\,{\text{Rs}}{\text{.}}\,{\text{100}} \cr & {\text{After}}\,{\text{paying}}\,{\text{to}}\,{\text{charity,}}\,{\text{A's}}\,{\text{share}} \cr & = Rs.\,\left( {95 \times \frac{3}{5}} \right) = Rs.\,57 \cr & {\text{If}}\,{\text{A's}}\,{\text{share}}\,{\text{is}}\,Rs.\,57, \cr & {\text{Total}}\,{\text{profit}} = Rs.\,100 \cr & {\text{If}}\,{\text{A's}}\,{\text{share}}\,Rs.\,855, \cr & {\text{Total}}\,{\text{profit}} \cr & = {\frac{{100}}{{57}} \times 855} \cr & = 1500 \cr} $$

For managing, A received = 5% of Rs. 7400 = Rs. 370.
Balance = Rs. (7400 - 370) = Rs. 7030.
Ratio of their investments = (6500 x 6) : (8400 x 5) : (10000 x 3)
= 39000 : 42000 : 30000
= 13 : 14 : 10
$$\eqalign{ & \therefore {\text{ B's Share}} \cr & = {\text{Rs}}{\text{. 7030}} \times \frac{{14}}{{37}} \cr & = {\text{Rs}}{\text{. 2660}} \cr} $$

Ratio of initial investments
$$\eqalign{ & = {\frac{7}{2}:\frac{4}{3}:\frac{6}{5}} \cr & = 105:40:36 \cr} $$
Let the initial investments be 105x, 40x and 36x
$$\left( {105x \times 4 + \frac{{150}}{{100}} \times 105x \times 8} \right)$$      $$:$$ $$\left( {40x \times 12} \right)$$   $$:$$ $$\left( {36x \times 12} \right)$$
$$\eqalign{ & = 1680x:480x:432x \cr & = 35:10:9 \cr & {\text{Hence,}}{\kern 1pt} {\text{B's}}{\kern 1pt} {\text{share}} \cr & = {\text{Rs}}{\text{.}}\left( {21600 \times \frac{{10}}{{54}}} \right) \cr & = {\text{Rs}}{\text{.}}\,4000 \cr} $$

$$\eqalign{ & {\text{Let}}\,C = x \cr & {\text{Then,}}\,{\text{B}} = x + 50000\,{\text{and}} \cr & {\text{A}} = x + 50000 + 40000 \cr & \,\,\,\,\,\,\,\, = x + 90000 \cr & So,\,x + x + 50000 + x + 90000 = 500000 \cr & \Rightarrow 3x = 360000 \cr & \Rightarrow x = 120000 \cr & {\text{A:B:C}} = 210000:170000:120000 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 21:17:12 \cr & \therefore {\text{A's}}\,{\text{share}} \cr & = Rs.\,\left( {350000 \times \frac{{21}}{{50}}} \right) \cr & = Rs.\,1,47,000 \cr} $$

$$\eqalign{ & {\text{Let their investments be}}\, \cr & Rs.\,x\,{\text{for}}\,{\text{14}}\,{\text{months}},\, \cr & Rs.\,y\,{\text{for}}\,{\text{8}}\,{\text{months}}\,{\text{and}}\, \cr & Rs.\,z\,{\text{for}}\,{\text{7}}\,{\text{months}}\,{\text{respectively}}. \cr & {\text{Then}},\,14x:8y:7z = 5:7:8 \cr & {\text{Now}},\frac{{14x}}{{8y}} = \frac{5}{7} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,98x = 40y \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,y = \frac{{49}}{{20}}x \cr & {\text{And}},\frac{{14x}}{{7z}} = \frac{5}{8} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,112x = 35z \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,z = \frac{{112}}{{35}}x = \frac{{16}}{5}x \cr & \therefore x:y:z \cr & = x:\frac{{49}}{{20}}x:\frac{{16}}{5}x \cr & = 20:49:64 \cr} $$

Let B's capital be Rs. x
∴ A's share in 12 months = 3500 × 12
And, B's share in 7 months = 7x
$$\eqalign{ & {\text{Then}},\, {\frac{{3500 \times 12}}{{7x}} = \frac{2}{3}} \cr & \Rightarrow 14x = 126000 \cr & \Rightarrow x = 9000 \cr} $$

  $$A:B$$
  $$ = \left[ {4x \times 3 + \left( {4x - \frac{1}{4} \times 4x} \right) \times 7} \right]$$       $$:$$ $$\left[ {5x \times 3 + \left( {5x - \frac{1}{5} \times 5x} \right) \times 7} \right]$$
$$\eqalign{ & = \left( {12x + 21x} \right):\left( {15x + 28x} \right) \cr & = 33x:43x = 33:43 \cr & \therefore {\text{A's share}} = {\text{Rs}}{\text{.}}\left( {760 \times \frac{{33}}{{76}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,330 \cr} $$

Let initial investment of A is 3x and B is 5x, then C investment is also 5x, but most important to note in this question is the time duration of investment
Like, A invested for 12 months, B invested for 12 months and C invested for 6 months.

A : B : C = (3x x 12) : (5x x 12) : (5x x 6)
= 36 : 60 : 30
= 6 : 10 : 5.

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

$$\eqalign{ & A:B:C \cr & = \left( {20000 \times 24} \right):\left( {15000 \times 24} \right):\left( {20000 \times 18} \right) \cr & = 4:3:3 \cr & \therefore {\text{B's}}\,{\text{share}} = Rs.\,\left( {25000 \times \frac{3}{{10}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,7500 \cr} $$