A woman distributed her savings among her daughters A, B, C and D in the ratio…

Concept

When quantities are divided in a ratio, write each quantity as its ratio part multiplied by one common value. A transfer subtracts the amount from the giver and adds the same amount to the receiver.

The new ratio then forms an equation in the common value. Solve that equation first, and only afterward calculate the requested initial total.

Application

1. Let the common value be x. The initial shares follow this mapping:

   Daughter	Initial share
   A	6x
   B	7x
   C	9x
   D	16x

2. After A transfers ₹600 to C, their shares become A = 6x − 600 and C = 9x + 600.

3. Use the resulting ratio A : C = 1 : 2: (6x − 600) / (9x + 600) = 1 / 2.

4. Cross-multiply and simplify: 2(6x − 600) = 9x + 600, so 12x − 1,200 = 9x + 600, hence 3x = 1,800 and x = 600.

5. The requested initial total is A + B + C = (6 + 7 + 9)x = 22 × 600 = ₹13,200.

Cross-check

With x = 600, the initial shares of A, B and C are ₹3,600, ₹4,200 and ₹5,400. After the transfer, A has ₹3,000 and C has ₹6,000, whose ratio is 1 : 2; their initial total is ₹13,200.