This is a question written by someone who doesn't know much about finance. We wouldn't usually talk about shares of an index member, but perhaps the weight of each member in an index, i.e. a cap weighting or a price weighting. We would talk about shares of stock in a portfolio; let's substitute portfolio for index and interpret the question that way.
We'd also usually talk about the change in the stock prices from the close of the previous day, not usually from today's open. OK, enough correcting the question.
So at the open we're long 2000 X @ 3.80, 1000 Y @ 3.50 and 3000 Z @ 4.30. The value of this portfolio at the open is
[tex]2000 \times 3.80 + 1000 \times 3.50 + 3000 \times 4.30 = \$24,000[/tex]
At the end of the day we're told we've made 5.4% so our portfolio is valued at
[tex]24,000 \times 1.054 = \$25,296 \approx \$25,300[/tex]
5.4% is what pros call a good day.
