Partnership - 03

Explanation:-

Ratio of investments of A, B and C = Ratio of their profits
$$\eqalign{ & = 337.50:1125:63.50 \cr & = 9:30:17 \cr & \therefore {\text{A's investment}} \cr & = {\text{Rs}}{\text{.}}\left( {14000 \times \frac{9}{{56}}} \right) \cr & = {\text{Rs. }}{\text{2250}} \cr & {\text{B's investment}} \cr & = {\text{Rs}}{\text{.}}\left( {14000 \times \frac{{30}}{{56}}} \right) \cr & = {\text{Rs. }}{\text{7500}} \cr & {\text{Hence, required difference}} \cr & = {\text{Rs}}{\text{.}}\left( {7500 - 2250} \right) \cr & = {\text{Rs. }}{\text{5250}} \cr}$$

Explanation:-

$$\eqalign{ & {\text{Let C}} = x \cr & {\text{Then, B}} = x + 5000{\text{ and}} \cr & {\text{A}} = x + 5000 + 4000 = x + 9000 \cr & {\text{So, }} \cr & \Rightarrow x + x + 5000 + x + 9000 = 50000 \cr & \Rightarrow 3x = 36000 \cr & \Rightarrow x = 12000 \cr & \therefore {\text{A}}:{\text{B}}:{\text{C}} \cr & = 21000:17000:12000 \cr & = 21:17:12 \cr & \therefore {\text{A's share}} \cr & = {\text{Rs}}{\text{.}}\left( {35000 \times \frac{{21}}{{50}}} \right) \cr & = {\text{Rs.}}{\text{14700}} \cr}$$

Explanation:-

A : B : C
(5000 × 4 + 2500 × 8) : (4500 × 6 + 3000 × 6) : (7000 × 6)
= 40000 : 45000 : 42000
= 40 : 45 : 42
$$\eqalign{ & \therefore {\text{A's share}} \cr & = {\text{Rs}}{\text{.}}\left( {5080 \times \frac{{40}}{{127}}} \right) \cr & = {\text{Rs}}{\text{.}}\,{\text{1600}} \cr & \therefore {\text{B's share}} \cr & = {\text{Rs}}{\text{.}}\left( {5080 \times \frac{{45}}{{127}}} \right) \cr & = {\text{Rs}}{\text{.}}\,{\text{1800}} \cr & \therefore {\text{C's share}} \cr & = {\text{Rs}}{\text{.}}\left( {5080 \times \frac{{42}}{{127}}} \right) \cr & = {\text{Rs}}{\text{.}}\,{\text{1680}} \cr}$$

Explanation:-

$$\eqalign{ & {\text{Here}}\,{{\text{p}}_1}:{{\text{p}}_2}:{{\text{p}}_3} = 5:3:12 \cr & {\text{and}}\,{{\text{x}}_1}:{{\text{x}}_2}:{{\text{x}}_3} = 5:6:8 \cr & {\text{According}}\,{\text{to}}\,{\text{the}}\,{\text{formula}} \cr & {\text{Required}}\,{\text{ratio}} \cr & = \frac{{{{\text{p}}_1}}}{{{{\text{x}}_1}}}:\frac{{{{\text{p}}_2}}}{{{{\text{x}}_2}}}:\frac{{{{\text{p}}_3}}}{{{{\text{x}}_3}}} \cr & = \frac{5}{5}:\frac{3}{6}:\frac{{12}}{8} \cr & = 1:\frac{1}{2}:\frac{3}{2} \cr & = 2:1:3 \cr & \cr & {\bf{Alternate:}} \cr & {\text{Profit}} = {\text{Time}} \times {\text{Capital invested}} \cr & {\text{Time}} = \frac{{{\text{Profit}}}}{{{\text{Capital invested}}}} \cr & {\text{Required ratio of time}} \cr & = \frac{5}{6}:\frac{3}{6}:\frac{{12}}{8} \cr & = 1:\frac{1}{2}:\frac{3}{2} \cr & = 2:1:3 \cr}$$

Explanation:-

$$\eqalign{ & {\text{Subhas}}:{\text{Aditya}} \cr & = \left( {25000 \times 36} \right):\left( {15000 \times 6 + 30000 \times 24} \right) \cr & = 900000:810000 \cr & = 10:9 \cr & \therefore {\text{Aditya's share}} \cr & \Rightarrow {\text{Rs}}{\text{.}}\left( {247000 \times \frac{9}{{19}}} \right) \cr & \Rightarrow {\text{Rs}}{\text{.117000}} \cr}$$

Explanation:-

A : B : C
= (25 lakhs × 1) + 35 lakhs × 2) : (35 lakhs × 2 + 25 lakhs × 1) : (30 lakhs × 3)
= 95 lakhs : 95 lakhs : 90 lakhs
= 19 : 19 : 18

Explanation:-

A : B : C
(40000 × 36) :(80000 × 12 + 40000 × 24) : (120000 × 24 + 40000 × 12)
= 144 : 192 : 336
= 3 : 4 : 7

Explanation:-

	1st Partner		2nd Partner
Capital →	12500	:	8500
	25	:	17
		8

According to the question,
Note: 60% of profit should be divided equally between them
$$\eqalign{ & {\text{8 units}} = {\text{Rs}}{\text{.}}\,{\text{300}} \cr & {\text{1 unit}} = {\text{Rs}}{\text{.}}\,\frac{{{\text{300}}}}{8} \cr & {\text{42 units}} = {\text{Rs}}{\text{.}}\,\frac{{300 \times 42}}{8} \cr & 40\% {\text{ of profit}} \cr & = {\text{Rs}}{\text{.}}\,\frac{{300 \times 42}}{8} \cr & 100\% {\text{ profit}} \cr & = {\text{Rs}}.\,\frac{{300 \times 42 \times 100}}{{8 \times 40}} \cr & = {\text{Rs}}{\text{.}}\,{\text{3937}}{\text{.50}} \cr}$$

Explanation:-

Let the capitals of Y was used for T months
According to the question,
$$\eqalign{ & \frac{{5 \times 8}}{{6 \times {\text{T}}}}{\text{ = }}\frac{5}{9} \cr & \Rightarrow {\text{T}} = {\text{12 months}} \cr}$$
Hence capital of Y was used for = 12 months

Explanation:-

Let the money invested by A, B and C be Rs. x, Rs. 2x and Rs. 3x respectively
Then, A : B : C
$$\eqalign{ & = \left( {x \times 12} \right):\left( {2x \times 6} \right):\left( {3x \times 4} \right) \cr & = 12x:12x:12x \cr & = 1:1:1 \cr & \therefore {\text{C's share}} \cr & = {\text{Rs}}{\text{.}}\left( {27000 \times \frac{1}{3}} \right) \cr & = {\text{Rs. }}{\text{9000}} \cr}$$