A ball is projected vertically up from ground. Boy $\text{'}A\text{'}$ standing at the window of first floor of a nearby building observes that the time interval between the ball crossing him while going up and the ball crossing him while going down is $2 \mathrm{s}$. Another boy $B$ standing on the second floor notices the time interval between the ball passing him twice, during up and down motion is $1 \mathrm{s}$. Calculate the difference between the vertical positions of boy $\mathrm{B}$ and boy $A$. (Assume $\mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}$)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.