Question

Two persons are walking beside a railway track at respective speeds of 2 and 4 km per hour in the same direction. A train came from behind them and crossed them in 90 and 100 seconds, respectively. The time, in seconds, taken by the train to cross an electric post is nearest to

• A. 87
• B. 82
• C. 75
• D. 78

Answer 1

The Correct Option is B

The correct option is (B): \(82\)

Let the length of the train be l and its speed be \(s\). 

Given \(\frac{l}{(s-2)×\frac{5}{18}} = 90; \frac{l}{(s-4) ×\frac{5}{18}} = 100\)

\(⇒ 90(s - 2)×\frac{5}{18} = 100(s - 4)×\frac{5}{18} ⇒ s = 22\)

∴ Length of the train =\(500\) m.

Hence the required time to cross a lamp post = \(\frac{500}{22×\frac{5}{18}}\)

i.e., \(81.81\) (or) \(82\) sec.

Answer 2

Let the length of the train be \(l\) km and the speed be \(s\) km/h. 
According to the question,
\(\frac {l}{s-2}=\frac {90}{3600}\)       ……….. (i)

\(\frac {l}{s-4}=\frac {100}{3600}\)       ………. (ii)
On dividing eq (ii) by eq (i),
\(s= 22\ km/h\)
From eq (i),
\(l= \frac {90}{3600} \times 20\)

\(\frac ls =  90 × \frac {20}{22}\)

\(\frac ls  = 81.81\)

\(\frac ls ≃ 82\) seconds

So, the correct option is (B): \(82\)