A sum of Rs.4.800 is divided between A. B and C such that the ratio of the share of A to the combined share of B and C is 3 : 5 and C receives $$\frac57$$​ of what A and B together receive. The difference (in Rs.) of A‘s share and B's share is:

Correct option is B

Given:

Total sum = Rs. 4,800,

Ratio of A's share to the combined share of B and C = 3 : 5,

C receives $$\frac{5}{7}$$​ of what A and B together receive.

Solution:

A's share in terms of B and C

Let the combined share of B and C = 5x,

Then, A's share = 3x (since the ratio of A's share to the combined share of B and C is (3 : 5))

Total sum = A's share + B's share + C's share:

3x + 5x = 8x

8x = 4,800

x = $$\frac{4,800}{8}$$​ = 600

A's share = 3x = 3 $$\times$$​ 600 = 1,800,

Combined share of B and C = 5x = 5 $$\times$$​ 600 = 3,000

C's share in terms of A and B.

C receives $$\frac{5}{7}$$​ of what A and B together receive.

A and B together receive:

A's share + B's share = 1,800 + B's share

C's share = $$\frac{5}{7} \times$$(1,800 + B's share)

B's share + C's share = 3,000

B's share + $$\frac{5}{7} \times$$​ (1,800 + B's share) = 3,000

7 $$\times$$​ B's share + 5 $$\times$$​ (1,800 + B's share) = 21,000

7B + 9,000 + 5B = 21,000

12B + 9,000 = 21,000

12B = 12,000

B = 1,000

C's share = $$(\frac{5}{7}$$​$$\times$$​ (1,800 + 1,000)):

C's share = $$\frac{5}{7} \times$$​ 2,800 = 2,000

A's share = Rs. 1,800,

B's share = Rs. 1,000,

Difference:

1,800 - 1,000 = 800  

Alternate Method: 

C is not equal So that first equal C 

C = 35x , b =  21x , a = 25-21 = 4x 

Total A+B+C =  10x + 14x = 24x 

24x = 4800 

x = 200 

Difference 

A - B = 9x - (14x-9x) 

A - B = 9x - 5x   

A - B = 4x 

4x = 200$$\times4$$​  

= 800