Let the cost price (CP) per gram of rice be $C$ and the selling price (SP) per gram of rice be $S$. The problem states that the cost price of 120 g of rice is the same as the selling price of 150 g of it.
Calculating Rice Percentage Loss
Relationship between CP and SP
We can express this relationship mathematically:
Cost Price of 120 g = Selling Price of 150 g
$120 \times C = 150 \times S$
Finding the Ratio of CP to SP
To find the relationship between the prices, we rearrange the equation:
$\frac{C}{S} = \frac{150}{120}$
Simplifying the fraction:
$\frac{C}{S} = \frac{5}{4}$
This ratio indicates that for every $5$ units of cost price, the selling price is $4$ units. This implies a loss occurs.
Calculating Percentage Loss
The loss is the difference between the cost price and the selling price for a comparable amount.
Loss = CP - SP
Using the ratio, let CP = 5 units and SP = 4 units.
Loss = 5 units - 4 units = 1 unit
The percentage loss is calculated based on the cost price:
Percentage Loss = $\left( \frac{\text{Loss}}{\text{CP}} \right) \times 100\%
Percentage Loss = $\left( \frac{1 \text{ unit}}{5 \text{ units}} \right) \times 100\%
Percentage Loss = $\frac{1}{5} \times 100\%
Percentage Loss = 20\%
Conclusion
The percentage loss is 20%.
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