A sum of ₹4,200 is divided among A, B, C and D such that the share of B is equal to $$\frac{2}{3}$$​ of the share of C and the share of C is equal to $$\frac{9}{13}$$​ of the share of D. If the ratio of the share of A and B is 8 : 9, then the difference between the shares of B and D will be:

Correct option is B

Given

B = $$\frac{2}{3} C$$​​

C = $$\frac{9}{13} D$$​​

A : B = 8 : 9

Total = ₹4200

D – B = ?

Solution:

$$\frac{B}{C}$$ =  $$\frac{2}{3}$$ ; $$\frac{C}{D} = \frac{9}{13}$$ ; $$\frac{A}{B} = \frac{8}{9}$$

Total parts = 16 + 18 + 27 + 39 = 100 parts

Each part = $$\frac{4200}{100} = 42$$​​

B's share = $$18\times 42 = 756$$​​

D's share =  $$39 \times 42 = 1638$$​​

Thus:

D - B = 1638 - 756 = 882

Thus, the correct option is (b) ₹882