If those answers are given in the book, then I think that it's a misprint. Those cannot be the actual answers. Your answers seem correct to me.
A company employs 2410 people whose annual salaries are summarised as follows:
<10 10-20 20-30 30-40 40-50 50-60 60-80 80-100 >100 (i.e. 100-140)
16 31 502 642 875 283 45 12 4
First row: salary (in $1000)
Second row: number of staff
Find the upper and lower quartile.
This should be fairly straightforward, I drew a quick cumulative frequency graph, came up with 603rd term for the lower quartile, 1808th term for the upper quartile; this is correct right?
Anyway I got lower quartile around $30 130, upper quartile $47 700
But the answers turned out to be $15 420 and $23 520 respectively, i.e. almost exactly half of each of the values I found.
But how are those answers even possible, with the largest frequencies between 30 and 60? it just doesn't seem logical.