Rs. 5625 is divided among A, B and C in such a way that A receive \(\frac{1}{2}\) of the sum of B & C and B receive \(\frac{1}{4}\) of the sum of A & C. Find the amount received by A & B together.

Rs. 3000

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

⇒ A = \(\frac{1}{2}\)(B + C)  ⇒ A : (B + C) = 1 : 2  = 3(total)

⇒ B = \(\frac{1}{4}\)(A + C)  ⇒ B : (A + C) = 1 : 4 = 5 (total)

make the total equal,

⇒ A : (B + C) = 5 : 10  = 15 (total)

⇒ B : (A + C) = 3 : 12 = 15 (total)

Therefore,

A = 5, B = 3 & C = 15 -(5 + 3) = 7

A     :     B     :     C

5     :     3     :     7  = 15   

Here,

15 R = 5625 (given)

1R = 375

A + B = (5 + 3)R = 8R = 8× 375 = 3000