A certain sum (in ₹) is divided between A, B and C such that the ratio of shares of A and B is 3 : 1, that of B and C is 5 : 3 and that of C and D is also 5 : 3. If the difference between the shares of B and D is ₹1,280, then what is the difference (in ₹) of shares of A and C?

Correct option is C

Given:

​$$\text{A : B = 3 : 1} \\\text{B : C = 5 : 3} \\\text{C : D = 5 : 3} \\\text{B - D = ₹1280} \\\text{Find: A - C = ?}$$​​

Solution:

$$\textbf{Step 1: Let B = x} \Rightarrow A = 3x \\\text{From B : C = 5 : 3} \Rightarrow \frac{x}{C} = \frac{5}{3}\\ \Rightarrow C = \frac{3x}{5} \\\text{From C : D = 5 : 3}\\ \Rightarrow \frac{C}{D} = \frac{5}{3} \Rightarrow \frac{3x}{5D} = \frac{5}{3}\\\ \\ \Rightarrow D = \frac{9x}{25}\\[10pt]\textbf{Step 2: Use the difference B - D = ₹1280} \\x - \frac{9x}{25} = \frac{16x}{25} \\\ \\\frac{16x}{25} = 1280 \Rightarrow x = \frac{1280 \times 25}{16} = 2000\\[10pt]\textbf{Step 3: Find A and C} \\\ \\A = 3x = 3 \times 2000 = ₹6000 \\C = \frac{3x}{5} = \frac{3 \times 2000}{5} = ₹1200 \\\ \\\text{So, } A - C = ₹6000 - ₹1200 = ₹4800\\[10pt]$$

​Final Answer: (C) ₹4,800