Partnership - Aptitude MCQ Questions and Solutions with Explanations

Total capital invested by A in 1 year
$$\eqalign{ & = 12 \times 4000 \cr & = {\text{Rs}}{\text{. 48000}} \cr} $$
Total capital invested by B in 1 year
$$\eqalign{ & = 4 \times 6000 + 8 \times 8000 \cr & = 24000 + 64000 \cr & = {\text{Rs}}{\text{.}}\,{\text{88000}} \cr} $$
Total capital invested by C in 1 year
$$\eqalign{ & = 9 \times 8000 + 3 \times 6000 \cr & = 72000 + 18000 \cr & = {\text{Rs}}{\text{. 90000}} \cr} $$

	A	:	B	:	C
Capital	48000	:	88000	:	90000
	24	:	44	:	45

According to the question,
$$\left( {24 + 44 + 45} \right){\text{units}}$$     = $${\text{Rs}}{\text{.}}\,{\text{16950}}$$
$$\eqalign{ & {\text{113 units}} = {\text{Rs}}{\text{. 16950}} \cr & 1{\text{ unit}} = \frac{{16950}}{{113}}{\text{ = Rs}}{\text{. 150}} \cr & {\text{Hence,}} \cr & {\text{Profit of A}} = 150 \times 24 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,{\text{3600}} \cr & {\text{Profit of B}} = 150 \times 44 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,{\text{6600}} \cr & {\text{Profit of C}} = 150 \times 45 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,{\text{6750}} \cr} $$

Total profit = Rs. 4000
According to the question,
$$\eqalign{ & {\text{20% of B's capital}} = {\text{Rs}}{\text{.}}\,{\text{4000}} \cr & {\text{1% of B's capital}} = {\text{Rs}}{\text{.}}\,\frac{{{\text{4000}}}}{{20}} \cr & {\text{B's total capital}} \cr & = {\text{Rs}}{\text{. }}\frac{{{\text{4000}}}}{{20}} \times 100 \cr & = {\text{Rs}}{\text{. }}20000 \cr} $$
Let total capital required for business = 100 units.

	A	:	B	:	C
Capital	30	:	40	:	30
	× 500	:	× 500	:	× 500
	15000	:	20000	:	$$\boxed{15000}$$

Hence, Required capital for C = Rs. 15000

Note : In such type of question we can assume ratio as per our need to avoid fraction

Capital →	A 7 × 3	:	B 9 × 3
New Ratio, →	A 21x	:	B 27x

Total capital invested by A in 9 months
$$\eqalign{ & = 21x \times 3 + 7x \times 6 \cr & = 105x \cr} $$
Total capital of B invested in 9 months
$$\eqalign{ & = 27x \times 4 + 18x \times 5 \cr & = 198x \cr} $$
$$\eqalign{ & {\text{According to the question,}} \cr & \left( {105x + 198x} \right) = {\text{Rs}}{\text{. 10201}} \cr & 303x = {\text{Rs}}{\text{. 10201}} \cr & x = \frac{{10201}}{{303}} \cr & {\text{Hence,}} \cr & {\text{Share of A}} = 105 \times \frac{{10201}}{{303}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,3535 \cr & {\text{Share of B}} = 198 \times \frac{{10201}}{{303}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,{\text{6666}} \cr} $$

$$\eqalign{ & {\text{investment of A}} = 1000 \cr & {\text{So, investment of B}} + {\text{C}} \cr & = {\text{6000}} - 1000 \cr & = 5000 \cr & {\text{B}}:{\text{C}} = 5000 \cr & 2:3 = 2000:3000 \cr} $$
So,

A	:	B	:	C
1000	:	2000	:	3000
1	:	2	:	3 = 6

$$\eqalign{ & \therefore {\text{Profit of C}} = \frac{3}{6} \times 2400 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 1200 \cr} $$

$$\eqalign{ & {\text{Given share of }}{{\text{2}}^{{\text{nd}}}} \cr & = \frac{5}{{13}}{\text{of}}\left( {{{\text{1}}^{{\text{st}}}} + {{\text{3}}^{{\text{rd}}}}} \right) \cr & {\text{or, }}\frac{{{{\text{2}}^{{\text{nd}}}}}}{{{{\text{1}}^{{\text{st}}}}{\text{ + }}{{\text{3}}^{{\text{rd}}}}}} = \frac{5}{{13}} \cr & \therefore {1^{{\text{st}}}} + {{\text{2}}^{{\text{nd}}}} + {{\text{3}}^{{\text{rd}}}} = 13 + 5 = 18 \cr & \because 18{\text{units}} = 1620 \cr & \therefore {\text{1 unit}} = \frac{{1620}}{{18}} \cr & \therefore 5{\text{ units}} = \frac{{1620}}{{18}} \times {\text{5}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 4{\text{50}} \cr & {\text{Hence share of }}{{\text{2}}^{{\text{nd}}}} = {\text{Rs}}{\text{.}}\,{\text{450}} \cr} $$

∵ Loss will be divided according to their investment ratio =

A	:	B
3000	:	2400
5	:	4

$$\eqalign{ & {\text{Loss of B}} = \frac{4}{{\left( {5 + 4} \right)}} \times 720 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. 320}} \cr} $$

$$\eqalign{ & {\text{3A}} = {\text{4B}} \cr & {\text{B}} = {\text{2C}} \cr & \frac{{\text{A}}}{{\text{B}}} = \frac{4}{3} \cr & \frac{{\text{B}}}{{\text{C}}} = \frac{2}{1} \cr & {\text{A}}\,\,\,\,\,\,\,\,{\text{B}}\,\,\,\,\,\,\,\,{\text{C}} \cr & {\text{4}}\,\,\,\,\,\,\,\,\,\,{\text{3}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,{\text{2}}\,\,\,\,\,\,\,\,\,\,{\text{1}} \cr & \boxed{{\text{8}}\,\,:\,\,6\,\,\,:\,\,\,3\,} \cr} $$

Rs. 2209
x × x = 2209
x = 47

$$\eqalign{ & {\text{Let total profit}} = 100{\text{ unit}} \cr & 20\% {\text{ taken by C remaining profit}} \cr & = \frac{{100 \times 80\% }}{{100}} \cr & = 80{\text{ unit}} \cr & {\text{Ratio of money}} \cr} $$
\[\begin{array}{*{20}{c}} {\text{A}}&:&{\text{B}}&:&{\text{C}}&{} \\ {27,500}&{}&{32,500}&{}&{37,500}&{} \\ {11}&:&{13}&:&{15}&{ = 39{\text{ unit}}} \\ {}&{}&{}&{}&\begin{gathered} \,\,\,\,\,\,\,\,\,\, \downarrow _{39}^{ \times 80} \hfill \\ \hfill \\ \end{gathered} &\begin{gathered} \,\,\,\,\, \downarrow \hfill \\ \,\,\,\,80{\text{ unit}} \hfill \\ \end{gathered} \end{array}\]
$$\eqalign{ & \frac{{400}}{{13}}{\text{ unit}} = 13500 \cr & 1{\text{ unit}} = \frac{{135 \times 13}}{4} \cr & 100{\text{ unit}} = 135 \times 13 \times 25 = 43,875 \cr & {\text{Total profit}} = {\text{ Rs}}{\text{. 43,875}} \cr} $$

A : B
5 : 6
(5 × 4) + (4 × 8) : (6 × 4) + (8 × 8)
52 : 88
13 : 22
35 → 6.3
1 → $$\frac{{.9}}{5}$$
22 → 3.96