This question was previously asked in

NIMCET 2013 Official Paper

Option 3 : 90

NIMCET 2020 Official Paper

1447

120 Questions
480 Marks
120 Mins

Given:

A train takes 18 seconds to pass completely through a station 162 m long.

A train takes 15 seconds to pass completely through another station 120 m long.

**Concept:**

Time = Distance/speed

**Calculation:**

Let length of train be X m

Train cover total distance for passing 162 m station = (162 + X) m

Train cover total distance for passing 120 m station = (120 + X) m

Speed of train passing 162 m long station = Speed of train passing 120 m long station

⇒ \(\rm \frac {162 \ +\ X}{18} = \frac {120\ +\ X}{15}\)

⇒ 5(162 + X) = 6(120 + X)

⇒ 810 + 5X = 720 + 6X

⇒ X = 90 m

**∴ Length of train 90 m.**

Let the speed of train be x.

Let the length of train be L

Train cover total distance for passing 162 m station = (162 + L) m

⇒ ** **x × 18 = 162 + L

⇒ L = 18x - 162

Train cover total distance for passing 120 m station = (120 + L) m

⇒ x × 15 = 120 + L

⇒ 15x = 120 + 18x - 162

⇒ x = 14 m/sec

The length of train = 18 × 14 - 162 = 90 m

∴ Length of train 90 m.