CUET UG 2025 — General Test Arithmetic

Two trains of equal length are running in the same direction on parallel tracks. The slower train travels at 58 km/hr and the faster train travels at 73 km/hr.

Since both trains move in the same direction, the relative speed determines how fast the faster train gains on the slower train.

Relative Speed $= 73 - 58 = 15$=73−58=15 km/hr

---

The time is given in seconds and the answer is needed in meters, so the speed must be converted to m/s.

To convert km/hr to m/s, multiply by $\frac{5}{18}$185​:

$$15 \times \frac{5}{18}$$15×185​

$$= \frac{75}{18}$$=1875​

$= \frac{25}{6}$=625​ m/s

---

When the faster train completely passes the slower train, it must cover the length of both trains. Since both trains have equal length $L$L:

Total distance covered $= L + L = 2L$=L+L=2L

---

Using the relationship between distance, speed, and time:

$$2L = \frac{25}{6} \times 144$$2L=625​×144

$$2L = \frac{25 \times 144}{6}$$2L=625×144​

$$2L = \frac{3600}{6}$$2L=63600​

$$2L = 600$$2L=600

$L = 300$L=300 meters

Therefore, each train is 300 meters long.