The C.P. of an article is $40\%$ of the S.P. The percent that the S.P. is of C.P. is

### Concept & Percentage Ratios When comparing two values, the question "what percent is A of B" translates algebraically to $\frac{A}{B} \times 100$. This directly evaluates the ratio between the two numbers as a percentage of the base value B. $$ \text{Required \%} = \frac{\text{Target Value}}{\text{Base Value}} \times 100 $$ ### Step-by-Step Solution * Given: Cost Price (C.P.) is $40\%$ of Selling Price (S.P.). * Mathematically: $C.P. = 0.40 \times S.P.$ * Let S.P. be $100$ units. * Then, C.P. = $40\% \text{ of } 100 = 40$ units. * The question asks for the percent that S.P. is of C.P. * Here, S.P. is the target value ($100$) and C.P. is the base value ($40$). * Calculate Percentage: $(\frac{S.P.}{C.P.}) \times 100$ * Substitute the values: $(\frac{100}{40}) \times 100$ * Simplify: $\frac{100}{40} = 2.5$. * Multiply: $2.5 \times 100 = 250\%$. ### Exam Strategy & Shortcut Convert $40\%$ to a fraction: $40\% = \frac{2}{5}$. So, $C.P. = \frac{2}{5} S.P.$ Rearrange to find the ratio of S.P. to C.P.: $\frac{S.P.}{C.P.} = \frac{5}{2}$. Convert the fraction $\frac{5}{2}$ back to a percentage by multiplying by 100: $\frac{5}{2} \times 100 = 250\%$. ### Common Pitfall Misinterpreting the question as asking for the *profit* percentage. If the question asked for profit percentage, it would be $\frac{100 - 40}{40} = 150\%$. However, it simply asks what percent the S.P. is relative to the C.P. ### Final Answer Therefore, the correct answer is **250**.