### PARTNERSHIP

1. Explanation :

Ratio of shares of A, Band C = Ratio of their investments = 120000 : 135000 : 150000 = 8 : 9 : 10.
A’s share = Rs. (56700 * (8/27))= Rs. 16800.
B's share = Rs. ( 56700 * (9/27)) = Rs. 18900.
C's share = Rs. ( 56700 * (10/27))=Rs. 21000.

1. Explanation :

Clearly, Alfred invested his capital for 12 months, Peter for 9 months and Ronald for 3 months.
So, ratio of their capitals = (45000 x 12) : (60000 x 9) : (90000 x 3) = 540000 : 540000 : 270000 = 2 : 2 : 1.
Alfred's share = Rs. (16500 x (2/5)) = Rs. 6600
Peter's share = Rs. (16500 x (2/5)) = Rs. 6600
Ronald's share = Rs. (16500 x (1/5)) = Rs. 3300.

1. Explanation :

Ratio of the capitals of A, Band C = 20000 x 5 + 15000 x 7 : 20000 x 5 + 16000 x 7 : 20000 x 5 + 26000 x 7 = 205000:212000 : 282000 = 205 : 212 : 282.
A’s share = Rs. 69900 x (205/699) = Rs. 20500
B's share = Rs. 69900 x (212/699) = Rs. 21200;
C's share = Rs. 69900 x (282/699) = Rs. 28200.

1. Explanation :

. Let C's capital = Rs. x. Then, B's capital = Rs. (2/3)x
A’s capital = Rs. (3 x (2/3).x) = Rs. 2x.
Ratio of their capitals = 2x : (2/3)x :x = 6 : 2 : 3.
Hence, B's share = Rs. ( 6600 x (2/11))= Rs. 1200.

1. Explanation :

Ratio of shares of A, B, C, D = (24 x 3) : (10 x 5) : (35 x 4) : (21 x 3) = 72 : 50 : 140 : 63.
Let total rent be Rs. x. Then, A’s share = Rs. (72x)/325
(72x)/325=720
x=(720 x 325)/72 = 3250
Hence, total rent of the field is Rs. 3250.

1. Explanation :

Suppose B joined after x months.
Then, B's money was invested for (12 - x) (76000 x 12)/(57000 x (12-x) =2/1
912000=114000(12-x)
114 (12 - x) = 912
12-x=8
x=4
Hence, B joined after 4 months.

1. Explanation :

Let the initial investments of A, Band C be Rs. 3x, Rs. 2x and Rs. 4x respectively. Then, (3x x 36) : [(2x x 12) + (2x + 270000) x 24] : [(4x x 24) + (4x +270000) x 12]=3:4:5
1O8x : (72x + 6480000) : (144x + 3240000) = 3 : 4 : 5
108x /(72x+6480000)=3/4
432x = 216x + 19440000
216x = 19440000
x=90000
Hence, A’s initial investment = 3x = Rs. 2,70,000;
B's initial investment = 2x = Rs. 1,80,000;
C's initial investment = 4x = Rs. 3,60,000.