Two trains 'A' and 'B' of length ' l ' and ' 4l ' are travelling into a tunnel of length ' L ' in parallel tracks from opposite directions with velocities 108 km/h and 72 km/h, respectively. If train 'A' takes 35 s less time than train 'B' to cross the tunnel, then length ' L ' of tunnel is: (Given L = 60l) (a) 900 m (b) 1200 m (c) 1800 m (d) 2700 m

Answer: (c). vA = 108 km/h = 30 m/s, vB = 72 km/h = 20 m/s Time to cross tunnel: tA = (L + l)/(30), tB = (L + 4l)/(20) With L = 60l: 64l/20 - 61l/30 = 35 ⇒ 7l/6 = 35 ⇒ l = 30 m L = 60 × 30 = 1800 m, so the answer is (c).

Two trains 'A' and 'B' of length ' l ' and ' 4l ' are travelling into… | JEE Main 2023 (13 Apr, Shift 1)

Q6JEE Main 2023 · 13 APR · SHIFT 1Medium

Relative Velocity

Two trains 'A' and 'B' of length ' $l$ ' and ' $4l$ ' are travelling into a tunnel of length ' $L$ ' in parallel tracks from opposite directions with velocities $108\text{ km/h}$ and $72\text{ km/h}$ , respectively. If train 'A' takes $35\text{ s}$ less time than train 'B' to cross the tunnel, then length ' $L$ ' of tunnel is:

(Given $L = 60l$ )

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Answer: (c)

$v_A = 108\text{ km/h} = 30\text{ m/s}$ , $v_B = 72\text{ km/h} = 20\text{ m/s}$
Time to cross tunnel: $t_A = \frac{L + l}{30}$ , $t_B = \frac{L + 4l}{20}$
With $L = 60l$ : $\frac{64l}{20} - \frac{61l}{30} = 35 \Rightarrow \frac{7l}{6} = 35 \Rightarrow l = 30\text{ m}$
$L = 60 \times 30 = 1800\text{ m}$ , so the answer is (c).

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