If $A : B = 4 : 5$, $B : C = 7 : 9$ and $C : D = 3 : 4$, and if $A$'s share is ₹ 1680, the share of $D$ is

### Concept & Combining Ratios To find a continuous ratio $A:B:C:D$ from individual sequential ratios, align the common terms by finding equivalent ratios. ### Step-by-Step Solution 1. **Given:** $A : B = 4 : 5$, $B : C = 7 : 9$, $C : D = 3 : 4$. $A$'s share = ₹ 1680. 2. First, align $B$ in $A:B$ and $B:C$. Multiply $A:B$ by 7 and $B:C$ by 5: $A : B = 28 : 35$ and $B : C = 35 : 45$. So, $A : B : C = 28 : 35 : 45$. 3. Next, align $C$ in $A:B:C$ and $C:D$. $C$ is 45 in the first, and 3 in the second. Multiply $C:D$ by 15: $C : D = 45 : 60$. 4. Combined ratio: $A : B : C : D = 28 : 35 : 45 : 60$. 5. $A$'s share is $28x = 1680 \implies x = 60$. 6. $D$'s share is $60x = 60 \times 60 = 3600$. ### Exam Strategy & Shortcut We only need the relation between $A$ and $D$. We know $\frac{A}{D} = \frac{A}{B} \times \frac{B}{C} \times \frac{C}{D}$. $\frac{A}{D} = \frac{4}{5} \times \frac{7}{9} \times \frac{3}{4} = \frac{7}{15}$. If $A = 1680$, then $D = A \times \frac{15}{7} = 1680 \times \frac{15}{7} = 240 \times 15 = 3600$. ### Common Pitfall Trying to calculate all individual shares instead of directly computing the ratio between the required terms. ### Final Answer Therefore, the correct answer is **₹ 3600**.