A certain sum is divided between A, B, C and D such that the ratio of the shares of A and B is 1 : 3, that of B and C is 2 : 5, and that of C and D 2 : 3. If the difference the shares of A and C is Rs. 3,510, then the share of D is:

Solution (By Examveda Team)

According to the question
\[\begin{array}{*{20}{c}} {\text{A}}&:&{\text{B}}&:&{\text{C}}&:&{\text{D}} \\ 1&:&3&{}&{}&{}&{} \\ {}&{}&2&:&5&{}&{} \\ {}&{}&{}&{}&2&:&3 \end{array}\]
The ratio of the A : B : C : D is
⇒ (1 × 2 × 2) : (3 × 2 × 2) : (3 × 5 × 2) : (3 × 5 × 3)
⇒ 4 : 12 : 30 : 45
The difference between the share of A and C is
⇒ (30 - 4) units
⇒ 26 units
Now,
⇒ 26 units = 3510
⇒ 1 unit = $$\frac{{3510}}{{26}}$$
⇒ 1 unit = Rs. 135
The share of D is
⇒ 45 units
⇒ 45 × 135
⇒ 6075
The share of D is Rs. 6075