UPSC CDS I 2025 Mathematics Paper

Time =( Distance covered )∕( Speed )
When a train passes a station, distance covered = (Length of train + Length of station).
Calculation:
Case 1: Through station of length x
(L+x)∕v=t...‌ (i) ‌
Case 2: Through station of length y
(L+y)∕v=2t...‌ (ii) ‌
From (i): v=(L+x)∕t
From (ii): v=(L+y)∕(2t)
Equating both values of v :
‌(L+x)∕t=(L+y)∕(2t)
‌2(L+x)=(L+y)
‌2L+2x=L+y
‌L=y−2x...‌ (iii) ‌
Now, time to pass station of length (x+y) :
‌ Required time ‌=(L+(x+y))∕v
Using (i): v=(L+x)∕t
So, Required time =(L+x+y)∕((L+x)∕t)
=[(L+x+y)×t]∕(L+x)
Substitute L=y−2x :
‌=[(y−2x+x+y)×t]∕(y−2x+x)
‌=[(2y−x)×t]∕(y−x)