A sum of money is divided among $A$, $B$, $C$ and $D$ in the ratio of $3 : 4 : 9 : 10$ respectively. If the share of $C$ is ₹ 2580 more than the share of $B$, then what is the total amount of $A$ and $D$ together?

### Concept & Ratio Differences Instead of calculating the total sum first, you can use the numerical difference between specific ratio parts to find the monetary value of a single ratio unit. ### Step-by-Step Solution Given: * Ratio of shares $A:B:C:D = 3:4:9:10$ * $C$'s share - $B$'s share = ₹ 2580 1. Find the difference in ratio parts between $C$ and $B$: Difference in parts = $9 - 4 = 5 \text{ parts}$ 2. Equate this difference to the given monetary value: $5 \text{ parts} = 2580$ 3. Find the value of $1 \text{ part}$: $1 \text{ part} = \frac{2580}{5} = 516$ 4. Determine the total ratio parts for $A$ and $D$ together: Parts for $A + D = 3 + 10 = 13 \text{ parts}$ 5. Calculate the total amount for $A$ and $D$: Total amount = $13 \times 516$ Total amount = $6708$ ### Exam Strategy & Shortcut Identify that $5$ ratio units = $2580$, so $1$ unit = $516$. We need the sum of $A$ and $D$ ($3+10=13$ units). Calculate $13 \times 516$. To do this quickly, look at the unit digit: $3 \times 6 = 18$, so the answer must end in 8. Option (c) is the only explicit number ending in 8. Compute to confirm: $13 \times 500 = 6500$, $13 \times 16 = 208$, sum is $6708$. ### Common Pitfall Trying to find the entire total sum of money first by finding all parts, which wastes time and adds unnecessary calculation steps. ### Final Answer Therefore, the correct answer is **₹ 6708**.