A train overtakes two persons travelling in the direction of train with the speed of 5 km/h and 8 km/h in 20 seconds and 24 seconds respectively. Find the length (In meters) of the train.

GIVEN:

A train overtakes two persons travelling in the direction of train with the speed of 5 km/h and 8 km/h in 20 seconds and 24 seconds respectively

FORMULA USED:

Relative speed = (a + b) for opposite directions

Relative speed = (a - b) for same directions

Where a and b are speeds of train

Speed = Distance/Time

CALCULATION:

Let the length of train be l m and speed of train be v km/hr.

One person with speed 5 km/h is overtaken in 20 seconds

Relative speed = (v - 5) × (5/18) m/sec

⇒ (v - 5) × (5/18) = l/20

⇒ 20 × (v - 5) × (5/18) = l    --- (1)

Similarly, Second person with speed 8 km/h is overtaken in 24 seconds

⇒ (v - 8) × 5/18 = l/24

⇒ 24 × (v - 8) × 5/18 = l    --- (2)

Equating (1) and (2),

20 × (v - 5) × (5/18) = 24 × (v - 8) × 5/18

⇒ 20v - 100 = 24v - 192

⇒ 4v = 92

⇒ v = 23 km/hr

Substituting v in (2), we get

(23 - 8) × 5/18 = l/24

⇒ l = 100 m

∴ The length of the train is 100 meters.