A voltage of resistance 500ohms calibrated read 1ohm per division. If the instrument is required to read 10ohm per scale division, what series resistance must be connected to it

you want to reduce current in the meter by a factor of ten, so series impedance needs to be increased by a factor of ten. Honestly, your first sentence is just a tad confusing to me. Normally, one would claibrate a meter to read current per division.