Suppose A invested Rs. N.
Then A : B : C = 12N : 6 x (2N) : 4 x (3N) = 1 : 1 : 1
? C's share = Rs. (18000) x 1/3 = Rs. 6000
Ratio of capital in the beginning = 1/3 : 1/4 : 1/5 = 20 : 15 : 12.
Ratio of investment for the whole year = (20 x 4 + 10 x 8) : (15 x 12) : (12 x 12) = 40 : 45 : 36
? A's share = Rs. (847 x 40)/121 = Rs. 280
Total investment = (100/15) x 45000 = ? 300000
? Investment of Avinash : Investment of Manoj : investment of Arun = 3 : 2 : 5
? Investment of Manoj = (2/10) x 300000 = ? 60000
A's share : B's share
= 900 x 12 : 45000 x (12 - 6)
= 12 : 5 x 6 = 2 : 5
A's share : B's share
= Ratio of products of investment and time period of investment
= (4000 x 12) : 16000 x (12 - 3)
= 4 x 12 : 16 x 9
= 1 : 3
Note Here, the partnership is compound, in which A invested for 1 yr or 12 month and B invested 3 months later. it does mean B invested for (12 - 3) months.
Let investment of R = N
Then, investment of Q = 2N/3
and investment of P = 2N
? Ratio of capitals of P, Q and R = 2N : (2N/3) : N
= 6N : 2N : 3N = 6 : 2 : 3
A : B : C = 2000 x 12 : 3000 x 24 : 4000 x 24 = 1 : 3 : 4
A's share = Rs. 3200 x (1/8) = Rs. 400
Ratio of shares = 12000 x 24 : 16000 x 24 : 15000 x 16 = 6 : 8 : 5
? C's share = Rs. 45600 x (5/19) = Rs. 12000
Let the amount invested by Ramesh = Rs. N
Then, 20000 x 6 : 12N = 6000 : 3000
? 120000/12N = 2/1
? N = 5000
Suppose C invests Rs. N
Then B's investment = Rs. (N + 5000)
and A's investment = Rs. (N + 12000)
? N + (N + 5000) + (N + 12000) = 47000
? N = 10000
Thus A : B : C = 22000 : 15000 : 10000 = 22 : 15 : 10
? B's share = Rs. (9400 x 15)/47 = Rs. 3000
Let 6 (A's capital) = 8 (B's capital) = 10 (C's capital) = k
Then A's capital = k/6 B's capital = k/8
and C's capital = k/10
? Ratio of capitals of A, B, and C = (k/ 6) : (k/8) : (k/10) = 20 : 15 : 12.
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