AFCAT Model Paper 4

GIVEN: Length of the train = 240 m FORMULA: Length of the train = (Time taken to cross a man walking in the same direction) × (Speed of the train - Speed of the man) CALCULATION: Let the speed of the train be v km per hour Speed of train with respect to the walking man $= (v - 8) \times \frac{5}{18}$ $\Rightarrow \frac{5v-40}{18}$ -----(1) Speed of train with respect to the running man $= (v + 10) \times \frac{5}{18}$ $\Rightarrow \frac{5v+50}{18}$ ------(2) According to the question and from (1) $\left[ 240 \div \left\{ \frac{5v-40}{18} \right\} \right] = 12$ $\Rightarrow 240 \times 18 = 12 \times (5v - 40)$ ⇒ v – 8 = 72 ⇒ v = 80 km per hour Now, The required time to cross the running man $= \frac{240}{\left\{ \frac{5v+50}{18} \right\}}$ $\Rightarrow \frac{240 \times 18}{5 \times 80 + 50}$ ⇒ 9.6 seconds ∴ The required time is 9.6 seconds.