A certain sum is divided among A, B, C and D such that B' share is $$\frac{1}{3}$$ of A's share, C's share is 40% of B's share, and D's share is 50% of C's share. If the difference between the shares of B and D is ₹1600 then the sum is:

Let the share of A is 15Q

Given, 

• B's share is $$\frac{1}{3}^{rd}$$ of A's share.

i.e; B' share = $$\frac{15Q}{3}=5Q$$

• C's share is 40% of B's share.

i.e, C = $$\frac{40}{100}\times\ 5Q=2Q$$

• D'share is 50% of C's share.

i.e; D = $$\frac{50}{100}\times\ 2Q=1Q$$

Now, we have the ratio of A, B, C and D 

i.e 15Q : 5Q : 2Q : 1Q

The difference between the shares of B and D is ₹1600. (given)

so, 5Q - 1Q = ₹1600

; 4Q = ₹1600

1Q = ₹400

Total sum = 15Q + 5Q + 2Q + 1Q = 23Q

$$\therefore\ Total\ sum\ =\ 23\times\ 400=₹9200$$