Rs. 3,000 is divided among A, B and C in such that A receives \(\frac{1}{3}\) as much as B and C together receive and B receive \(\frac{2}{3}\) as much as A and C together receive. Find the share of C.

Rs. 1050

In these type of questions always note that the total amount/ratio must be same in all conditions.

⇒ A = \(\frac{1}{3}\)(B + C)  ⇒ A : (B + C) = 1 : 3  = 4(total)

⇒ B = \(\frac{2}{3}\)(A + C)  ⇒ B : (A + C) = 2 : 3 = 5(total)

make the total equal,

⇒ A : (B + C) = 5 : 15  = 20 (total)

⇒ B : (A + C) = 8 : 12 = 20 (total)

Therefore,

A = 5, B = 8 & C = 20 -(5 + 8) = 7

A     :     B     :     C

5     :     8     :     7  = 20  

Here,

20 R = 3000 (given)

1R = 150

C = 7R = 7× 150 = 1050