Certainly! Let's break down the problem step-by-step to find the percentage gain or loss for the trader.
1. Calculate the total cost of 100 oranges:
- The trader bought 100 oranges at the rate of 5 oranges for [tex]$1.20.
- First, determine the cost per orange: $[/tex](\[tex]$ 1.20 / 5) = \$[/tex] 0.24[tex]$ per orange.
- Therefore, the total cost for 100 oranges: $[/tex]100 \times \[tex]$ 0.24 = \$[/tex] 24.00[tex]$.
2. Calculate the number of oranges that were sold:
- From the 100 oranges, 20 got spoilt.
- Hence, the number of oranges sold: $[/tex]100 - 20 = 80[tex]$ oranges.
3. Calculate the total selling price of the sold oranges:
- The remaining 80 oranges were sold at the rate of 4 oranges for $[/tex]1.50.
- First, determine the selling price per orange: [tex]$(\$[/tex] 1.50 / 4) = \[tex]$ 0.375$[/tex] per orange.
- Therefore, the total revenue from selling 80 oranges: [tex]$80 \times \$[/tex] 0.375 = \[tex]$ 30.00$[/tex].
4. Calculate the gain or loss in monetary terms:
- Gain or loss is determined by the difference between the total revenue and the total cost.
- Gain (or loss) = Total Revenue - Total Cost
- Gain (or loss) = \[tex]$ 30.00 - \$[/tex] 24.00 = \[tex]$ 6.00
5. Calculate the percentage gain or loss:
- Percentage Gain (or Loss) = \( \left( \dfrac{\text{Gain (or Loss)}}{\text{Total Cost}} \right) \times 100 \)
- Percentage Gain = \( \left( \dfrac{\$[/tex] 6.00}{\$ 24.00} \right) \times 100 = 25\% \)
Therefore, the trader experienced a 25% gain.
The correct answer is B 25% gain.
