Relationships between Percentage change and inversely proportional numbers

[Jmq10]

Struggling with this.
I've a rate of $49 per hour based on a total hours of 350. If the hours are reduced then the rate increases. I have to work out the new rate based on 258 hours. Using inverse proportions I can work it out using (350/258)×49 = 66.47
However, the percentage change of the hours is worked out as (258-350)/350=0.26 or 26%
If we get 26% of $49 and then add it to the old rate it doesnt come out the same. Works out as $61.47.
I would have thought that if the hours were reduced by a fifth, the rate would have increased by a fifth. It works out if the hours are halved then the rate is doubled but this seems to be a one off. It seems that the percentage change is different for the two numbers even though they're proportionate. Could someone explain please...

 

[HallsofIvy]

There is nothing odd about that- and it doesn't really have anything to do with "indirect proportion". A percentage depends on the base and you are changing bases. If something starts at 1000 and decreases by 10% then it decreases by 1000*0.1= 100 so decreases to 1000- 100= 900. The base is 1000. If it now increases by 10% it increases by 10% of the new base, 900. 10% of 900 is 90 so it increases by 90 to 990, not the original 1000.