The labelled price of a cupboard is ₹ 6500. The shopkeeper sold it by giving 5% discount on the labelled price and earned a profit of 15%. What approximately is the cost price of the cupboard?

### Concept & MP to CP Ratio Connect Marked Price (MP) to Cost Price (CP) directly using the standard formula balancing the discount and profit margins: $\frac{\text{CP}}{\text{MP}} = \frac{100 - D\%}{100 + P\%}$. ### Step-by-Step Solution - Labelled Price (Marked Price, MP) = Rs. 6500. - Discount ($D\%$) = $5\%$. - Profit ($P\%$) = $15\%$. - Let the Cost Price be CP. - Using the formula: $\frac{\text{CP}}{6500} = \frac{100 - 5}{100 + 15}$. - $\frac{\text{CP}}{6500} = \frac{95}{115}$. - Simplify the fraction by dividing numerator and denominator by 5: $\frac{95}{115} = \frac{19}{23}$. - $\text{CP} = 6500 \times \frac{19}{23}$. - $\text{CP} = \frac{123500}{23} \approx 5369.56$. - The question asks for the approximate cost price. The calculated value $5369.56$ is closest to the option Rs. 5350 compared to the other available options. ### Exam Strategy & Shortcut $\text{SP} = 6500 \times 0.95$. $\text{CP} \times 1.15 = \text{SP}$. So, $\text{CP} = 6500 \times \frac{0.95}{1.15} = 6500 \times \frac{19}{23}$. $6500 / 23$ is roughly 282.6. $282.6 \times 19$ is approx $5370$. Looking at the options, 5350 is the only reasonable approximate value in that range. ### Common Pitfall Calculating the $15\%$ profit as a markdown from the Selling Price (i.e., taking $85\%$ of SP to find CP). Profit is a markup on CP, so you must divide by $1.15$, not multiply by $0.85$. ### Final Answer Therefore, the correct answer is **₹ 5350**.