A sum of ₹5200 is divided amongst A, B, C and D such that the ratio of shares of A and B is 2 : 3, that of B and C is 4: 5, and that of C and D is 1 : 2. What is the difference between the shares of B and D?

the ratio of shares of A and B is 2 : 3.

A : B = 2 : 3    Eq.(i)

that of B and C is 4: 5.

B : C = 4: 5    Eq.(ii)

Multiply Eq.(i) by 4 and Eq.(ii) by 3.

A : B : C = $$2\times4 : 3\times4 : 5\times3$$

= 8 : 12 : 15    Eq.(iii)

C and D is 1 : 2.

C : D = 1 : 2    Eq.(iv)

Multipluy Eq.(iii) by 1 and Eq.(iv) by 15.

A : B : C : D = 8 : 12 : 15 : $$15\times2$$

= 8 : 12 : 15 : 30

A sum of ₹5200 is divided amongst A, B, C and D.

So let's assume the share of A, B, C and D are 8y, 12y, 15y, 30y

8y+12y+15y+30y = 5200

65y = 5200

5y = 400

y = 80

difference between the shares of B and D = 30y-12y

= 18y

= $$18\times80$$

= ₹1440