Divide Rs. 5625 among A, B & C so that A may receive 1/2 as much as B & C and B 1/4 of what A and C together receive?

Divide Rs. 5625 among A, B & C so that A may receive 1/2 as much as B & C and B 1/4 of what A and C together receive? Correct Answer 1875, 1125, 2625

Let they receive A, B & C Rs. respectively. Now, A = (B + C) / 2 or,  2A = B + C - - - - - - - - - - (i) Again, B = (A + C) / 4 or, 4B = (A + C) or, 4B = (B + C) / 2 + C or, 4B = B/2 + C/2 + C or, 4B - B/2 = 3C/2 or, 7B/2 = 3C/2 or, B = 3C/7 - - - - - - - (ii) Now, 2A = 3C/7 + C  [from (i)] or, 2A = 10C/7 or, A = 5C/7 - - - - - - (iii) From (ii) and (iii),  B : C = 3 : 7 C : A = 7 : 5 So,  A : B : C = 5 : 3 : 7 A will receive = 5 / (5 + 3 + 7) × 5625 =  1875 Rs. B will receive = 3 / (5 + 3 + 7) × 5625 =  1125 Rs. C will receive = 7 / (5 + 3 + 7) × 5625 =  2625 Rs.
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