From which term should this AP start? Your friend Veer wants to participate in a 200 m race. He can currently run that distance in 51 seconds and with each day of practice it takes him 2 seconds less. He wants to do in 31 seconds.
What is the minimum number of days he needs to practice till his goal is achieved?
My question is what should be the first term of this AP? 51 or 49? Subsequently, what would be the answer? 11 or 10?
I would tell my reasoning but I don’t want to influence the answer.
EDIT: Okay, so my reasoning is this: since the question is asking how many days he needs to practice: we’ll start the AP, when he starts practising. And on his first day of practice, he can finish the race in 49s. Therefore, the AP should start with 49.
 A: You should start with $51$, since "What is the minimum number of days he needs to practice till his goal is achieved?" Questions like this usually assume that the start is "now" and we are given that he "currently" could run in $51$ seconds. So the answer should be $11$. I think what is wrong with your reasoning is that you thought that the AP should start when he starts practicing for one day. I will try to make a visualization:
Correct counting: $|\space\space\space |\space\space\space |...$
Your counting: $\space\space\space|\space\space\space|\space\space\space|$ You start with a space (doing the routine) and not a bar (end of previous routine and start of new routine). I hope you could understand what I'm trying to say.
A: I'm familiar with these questions. Trademark of lower level maths in India. According to my experience and the question a(initial term)=51 seconds
Then you have already solved the questions I guess.
P.S.
These types of questions are very general in AP of India, and the examiners expect us to blindlessly apply general term of AP formula. Taking the given value as first term.
According to the question the time given doesn't clearly specify what the starting point is.
