A sum of ₹ 1360 has been divided among $A$, $B$ and $C$ such that $A$ gets $\frac{2}{3}$ of what $B$ gets and $B$ gets $\frac{1}{4}$ of what $C$ gets. B's share is

### Concept & Formula Express the shares of A, B, and C as a combined ratio. Given: $$A = \frac{2}{3}B \implies \frac{A}{B} = \frac{2}{3}$$ $$B = \frac{1}{4}C \implies \frac{B}{C} = \frac{1}{4}$$ Combine these fractions to get the continuous ratio $A : B : C$. ### Step-by-Step Solution * **Align and combine ratios:** We have $A : B = 2 : 3$ and $B : C = 1 : 4$. To equalize the $B$ term across both ratios, multiply the $B : C$ ratio by 3: $$B : C = 3 : 12$$ Thus, the unified ratio is $A : B : C = 2 : 3 : 12$. * **Compute total units:** $$\text{Total Units} = 2 + 3 + 12 = 17 \text{ units}$$ * **Equate to total value to find 1 unit:** $$17 \text{ units} = 1360$$ $$1 \text{ unit} = \frac{1360}{17} = 80$$ * **Find B's share:** $$B = 3 \text{ units} = 3 \times 80 = 240$$ ### Exam Strategy & Shortcut Once you determine the unified ratio components $2:3:12$, notice that B's part is 3. The answer must be a multiple of 3. Looking at the options: * 120 (multiple of 3) * 160 (no) * 240 (multiple of 3) * 300 (multiple of 3) Execute the fast division: $\frac{1360}{17} = 80$. Then $3 \times 80 = 240$. ### Common Pitfall Mistaking the final ratio updates or incorrectly equating the fraction parts, yielding an incorrect unit value. Double-check your unified ratio by verifying if $B$ remains $\frac{1}{4}$ of $C$. Here, $\frac{3}{12} = \frac{1}{4}$, which confirms correctness. ### Final Answer **Therefore, the correct answer is ₹ 240.**