CONCEPT:RATIOS AND PARTNERSHIPS
-The share of an individual in the profit is in proportion to his investment made.
-If the investment of A and B are in the ratio a:b,then in the profit of x$, the shares of A and B are a/(a +b)*x $ and b/(a +b)*x $
respectively.
SOLUTION:
Let total investment be $100.
Then A's investment is 1/5*100= $20
Thus(B+C)'s investment=100-20=$80;-----(1)

Given, B=A+C
=>B-C=A=$20--------(2)
From (1) and (2) 2B=100=>B's investment is=$50
Hence C's investment is=100-(20+50)=30
Thus investment ratio of A:B:C =20:50:30=2:5:3
C's share thus is 3/10*5200=$1560 (C)

Hope this helps.
Devmitra Sen
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Let the total investment was 100.

A's invest: \(\frac{1}{5}\) * 100 = 20

Remanining: 100 - 20 = 80 (B +C)'s investment

=> B + C = 80 ---- Eqn(1)

B's investment= A + C = 20 + C

=> B - C = 20 ---- Eqn(2)

Eqn 1 + Eqn2: 2B = 100 or B = 50

=> B + C = 80

=> 50 + C = 80

=> C = 30

=> A: B: C = 20: 50: 30 or 2:5:3

C' share: \(\frac{3 }{ (2 + 5 + 3)}\) * 5,200

=> \(\frac{3}{10}\) * 5,200

=> 1,560

Answer C
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Let Total Capital invested be \(10\)

\(A : B : C = 2 : 5 : 3\)



C's share is \(\frac{3}{10}*520 = 1560\) , Answer must be (C)
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Since B equals the total of A and C, we can say that B is half of the total of A, B and C
Also, A is 1/5th of the total
Thus, it is best to assume the total of A, B and C to be a multiple of 2 and 5 (denominators) = 10
Thus: A = 10/5 = 2 and B = 10/2 = 5; hence C = 3
Ratio of A, B and C = 2 : 5 : 3

Thus, C = 5200 x 3/10 = 1560

Alt:
Since B equals the total of A and C, we can say that B is half of the total of A, B and C = 5200/2 = 2600
Also, A is 1/5th of the total = 5200/5 = 1040
Thus, C = 5200 - (1040 + 2600) = 1560

Answer C
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A share from the profit will be 1/5 of 5200 = 1040

B share from the profit is B = A +C so we can write B - C = 1040 --> 1

All three people share from the profit is A + B + C = 5200 from this we can find out B + C = 4160 ---> 2

Solving equation 1 and 2 we will get B as 2600 and C as 1560 . so our ans is C