When an article is sold for ₹ 116, the profit percent is thrice as much as when it is sold for ₹ 92. The cost price of the article is

### Concept & Proportional Profit Percentages When comparing two different profit percentages on the same item, they scale proportionally with the absolute profit amounts because the Cost Price base is identical. $$ \text{Profit } \%_2 = 3 \times \text{Profit } \%_1 \implies \text{Profit}_2 = 3 \times \text{Profit}_1 $$ ### Step-by-Step Solution * Let the Cost Price (C.P.) be $x$. * Profit$_1$ (selling at ₹ 92) = $92 - x$. * Profit$_2$ (selling at ₹ 116) = $116 - x$. * The problem states the profit percent is thrice as much. Since the C.P. is the same for both, the absolute profit is also thrice as much. * $116 - x = 3 \times (92 - x)$ * $116 - x = 276 - 3x$ * Add $3x$ to both sides and subtract $116$ from both sides: * $3x - x = 276 - 116$ * $2x = 160$ * $x = \frac{160}{2} = 80$. * The Cost Price is ₹ 80. ### Exam Strategy & Shortcut Option elimination works excellently here. Try option (d) ₹ 80: If $\text{C.P.} = 80$: Profit at $92 = 92 - 80 = 12$. Profit at $116 = 116 - 80 = 36$. Is $36$ thrice of $12$? Yes ($12 \times 3 = 36$). This matches the condition instantly, confirming ₹ 80 is the correct answer without solving equations. ### Common Pitfall Writing the equation with the multiplier on the wrong side, like $3 \times (116 - x) = (92 - x)$, is a standard logic error. Always read carefully: the larger profit is three times the smaller profit. ### Final Answer Therefore, the correct answer is **₹ 80**.