A sum of ₹12,000 is divided between A, B, C and D such that the ratio of shares of A and is 8 : 9, that of B and C is 2:3 and that of C and D is 9 : 13. What is the difference between the shares of B and D?

As per the given question,

The total amount of the sum =Rs. 12000

The share ratio of A and B $$=\dfrac{8}{9}=\dfrac{16}{18}$$

The Share ratio of B and C $$=2:3=\dfrac{18}{27}$$

The Share ratio of C and D $$=9:13=\dfrac{27}{39}$$

Hence the required ratio $$A:B:C:D=16:18:27:39$$

Hence the shares of A, B, C, and D $$16x+18x+27x+39=12000$$

$$\Rightarrow $$100x=12000$$

$$x=\dfrac{12000}{100}=120$$

Hence, the share of B $$=120\times 18=Rs. 2160$$

The share of D $$=39\times 120 =Rs. 4680$$

Hence, the required difference $$=4680-2160 =Rs. 2520$$