Can anyone explain the meaning of those 3 underlined blue lines, I can't understand them
Anyone can explain why they have taken assumption as 5 times not 6or7 times ????
In order for a zener diode to regulate at the maximum load current which will be required, then when it is unloaded the zener current must be at least equal to this maximum load current and ideally will be somewhat greater.
According to the NCERT textbook, 5 times the load current is a safe value.
For the last line, carbon resistors come in only certain values. Since 150 ohms is close to 167, and we are giving some tolerance for current, 150 ohm should suffice. Your final answer as 167 ohm will also be accepted, so not to worry about that.
Are these values given in ncert and should we have to remember them?
You don't have to remember them.