Certainly! Let's go through each part of the problem step-by-step.
### Total Watermelons
The total number of watermelons initially is 480 pieces.
### Day 1
The trader sold [tex]\(\frac{1}{2}\)[/tex] of the watermelons on the first day.
1. Number of watermelons sold on the first day:
[tex]\[
\text{Sold on first day} = \frac{1}{2} \times 480 = 240
\][/tex]
2. Number of watermelons remaining after the first day:
[tex]\[
\text{Remaining after first day} = 480 - 240 = 240
\][/tex]
### Day 2
The trader sold [tex]\(\frac{2}{5}\)[/tex] of the remaining watermelons on the second day.
1. Number of watermelons sold on the second day:
[tex]\[
\text{Sold on second day} = \frac{2}{5} \times 240 = 96
\][/tex]
2. Number of watermelons remaining after the second day:
[tex]\[
\text{Remaining after second day} = 240 - 96 = 144
\][/tex]
### Fraction Left to be Sold
(i) The fraction of watermelons left to be sold after the second day:
[tex]\[
\text{Fraction left to be sold} = \frac{\text{Remaining watermelons}}{\text{Initial watermelons}} = \frac{144}{480} = \frac{3}{10} = 0.3
\][/tex]
### Number of Watermelons Left to be Sold
(ii) The number of watermelons left to be sold after the second day:
[tex]\[
\text{Number of watermelons left} = 144
\][/tex]
### Percentage of Watermelon Left after accounting for Rotten Ones
After the second day, 8 of the remaining watermelons got rotten.
1. Number of good watermelons left after accounting for the rotten ones:
[tex]\[
\text{Good watermelons left} = 144 - 8 = 136
\][/tex]
2. Percentage of watermelons left:
[tex]\[
\text{Percentage left} = \left( \frac{136}{480} \right) \times 100 \approx 28.33\%
\][/tex]
So, summarizing:
- (i) The fraction of watermelons left to be sold is [tex]\(0.3\)[/tex] or [tex]\(\frac{3}{10}\)[/tex].
- (ii) The number of watermelons left to be sold is 144.
- (iii) The percentage of watermelons left after accounting for the 8 rotten ones is approximately [tex]\(28.33\%\)[/tex].
