Amit bought $10\,\text{kg}$ of apple for $\text{Rs}\,42.5$ and was cheated by shopkeeper by $6.25\%$ on market price but while selling the same at the market price he uses $12.5\%$ less weight. Find the total profit earned by Amit by selling $8\,\text{kg}$ of apple

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Grade 7

Multi-step problems with percents

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Q. Amit bought

10\,\text{kg}

of apple for

\text{Rs}\,42.5

and was cheated by shopkeeper by

6.25\%

on market price but while selling the same at the market price he uses

12.5\%

less weight. Find the total profit earned by Amit by selling

8\,\text{kg}

of apple

Calculate Cost per kg: Calculate the actual cost per kg of apples Amit paid. $\newline$ Amit bought $10\,\text{kg}$ of apples for Rs $42.5$ . To find the cost per kg, we divide the total cost by the total weight. $\newline$ $\frac{42.5}{10} = 4.25$ $\newline$ Cost per kg = Rs $4.25$
Calculate Market Price: Calculate the market price per kg of apples from which Amit was cheated. $\newline$ Amit was cheated by $6.25\%$ on the market price. To find the market price, we need to calculate the price before the cheating occurred. $\newline$ Let the market price be $x$ . Then, $93.75\%$ of $x$ is equal to the cost per kg Amit paid. $\newline$ $0.9375 \times x = 4.25$ $\newline$ $x = \frac{4.25}{0.9375}$ $\newline$ $x = 4.5333$ (approx) $\newline$ Market price per kg = Rs $4.5333$
Calculate Selling Price: Calculate the selling price per kg of apples using the market price. $\newline$ Amit sells the apples at the market price, which we calculated as Rs $4.5333$ per kg. $\newline$ Selling price per kg = Rs $4.5333$
Calculate Effective Weight: Calculate the effective weight Amit uses when selling the apples. $\newline$ Amit uses $12.5\%$ less weight when selling the apples. This means he only gives $87.5\%$ of the actual weight. $\newline$ For $1\,\text{kg}$ , the effective weight Amit uses is: $\newline$ $1 \times 0.875 = 0.875\,\text{kg}$
Calculate Total Weight: Calculate the total weight Amit would use when selling $8\,\text{kg}$ of apples. $\newline$ If Amit were to sell $8\,\text{kg}$ of apples using the reduced weight, he would actually be selling: $\newline$ $8 \times 0.875 = 7\,\text{kg}$
Calculate Total Revenue: Calculate the total revenue Amit would get from selling $8\,\text{kg}$ of apples at the market price. $\newline$ Using the market price per kg and the effective weight, the total revenue is: $\newline$ $7 \times 4.5333 = 31.7331$ (approx) $\newline$ Total revenue = Rs $31.7331$
Calculate Total Cost: Calculate the total cost of $8\,\text{kg}$ of apples at the cost price Amit paid. $\newline$ The cost price per kg is Rs $4.25$ , so for $8\,\text{kg}$ , the total cost is: $\newline$ $8 \times 4.25 = 34$ $\newline$ Total cost = Rs $34$
Calculate Profit: Calculate the profit Amit makes by selling $8\,\text{kg}$ of apples. $\newline$ Profit is the total revenue minus the total cost. $\newline$ Profit $= 31.7331 - 34$ $\newline$ Profit $= -2.2669$ $\newline$ This indicates a loss, which means there is a math error in the previous steps.