Two trains are moving in the same direction along parallel tracks. One of them is $200 \mathrm{m}$ long travelling with a velocity of $20 \mathrm{m} {\mathrm{s}}^{-1}$. The second one is $800 \mathrm{m}$ long travelling with a velocity of $7.5 \mathrm{m} {\mathrm{s}}^{-1}$. The time taken for the first train to overtake the second is

• A

  $20 \mathrm{s}$
• B

  $40 \mathrm{s}$
• C

  $60 \mathrm{s}$
• Correct answer
  D

  $80 \mathrm{s}$

Solution

From the figure, the relative displacement is



${\mathrm{s}}_{\mathrm{r}\mathrm{e}\mathrm{l}}=\left(800+200\right)\mathrm{m}=1000\mathrm{ }\mathrm{m}$

${\mathrm{\upsilon }}_{\mathrm{r}\mathrm{e}\mathrm{l}}={\mathrm{\upsilon }}_1-{\mathrm{\upsilon }}_2=\left(20-7.5\right)\mathrm{ }\mathrm{m} {\mathrm{s}}^{-1}$

$=12.5\mathrm{ }\mathrm{m} {\mathrm{s}}^{-1}$

$\therefore \mathrm{t}=\frac{{\mathrm{s}}_{\mathrm{r}\mathrm{e}\mathrm{l}}}{{\mathrm{\upsilon }}_{\mathrm{r}\mathrm{e}\mathrm{l}}}=\frac{1000}{12.5}=80\mathrm{ }\mathrm{s}$

Hence, the correct answer is option: 'D'.