A sum of Rs. 6,300 is divided among A, B, C and D such that the ratio of the combined share of A and D to the combined share of B and C is 11:10 and the ratio of the shares of B and D is 8:9. If C receives Rs. 1,560, then what is the difference (in Rs.) between the shares of A and B?

Total sum = Rs. 6,300.
The ratio of (A+D):(B+C)=11:10.
Total parts = 11+10=21 units.

21 units=6300⟹1 unit=300
Therefore:

A+D=11×300=3300
B+C=10×300=3000
Given that C receives Rs. 1,560:

B+1560=3000⟹B=3000−1560=1440
The ratio of the shares of B and D is 8:9:

D
B
​
=
9
8
​

D
1440
​
=
9
8
​
⟹D=
8
1440×9
​
=180×9=1620
Now, substituting the value of D into (A+D)=3300:

A+1620=3300⟹A=3300−1620=1680
We need to find the difference between the shares of A and B:

Difference=A−B=1680−1440=Rs. 240