A sum (in ₹) is distributed between A, B and in the ratio 9 : 6: 11. If A gives ₹500 from his share to C, the ratio of shares of A, B and C becomes 4 : 3 : 6. What is the sum ofshares(in ₹) of B and C, in the beginning?

In the first time, it will be A, B, and C ( where C is not printed )

Let us assume the share distributed between A, B, and C = $$9x, 6x, and 11x $$(where x is proportional constant)

Now A gives 500 to C and the ratio of shares becomes = 4:3:6 

$$\Rightarrow (9x-500): 6x : (11x+500) = 4:3:6 $$

calculating A and 'C's share 

$$ \dfrac{9x-500}{11x+500} =\dfrac {4}{6}  = \dfrac {2}{3}$$

$$\Rightarrow 27x - 1500 = 22x + 1000 $$

$$\Rightarrow 5x = 2500 $$

$$\Rightarrow x= 500 $$

At beginning B got = $$ 6 \times 500 = 3000$$

A got =$$ 9\times 500 = 4500 $$

C got =$$ 11 \times 500 = 5500 $$

Sum of share B and C = 3000 + 5500 = 8500 Ans