Question

A, B and C start from the same place and travel the same directions at speeds of 30, 40 and 60 km/hr respectively. B starts two hours after A. If B and C overtake A at the same instant how many hours after A did C start ?

• A. $3$
• B. $3.5$
• C. $4$
• D. $4.5$

Answer 1

Answer: (C)

$4$

B starts when A has already travelled for 2 hours and covered a distance = (2 x 30) km = 60 km

$\therefore$ Time taken by B to cover A with a relative speed of (40 - 30) km/hr = 10 km/hr = $\frac{60}{10}hrs=6hrs$

$\therefore$ When B overtakes A, A has travelled for 8 hrs and B for 6 hrs

It is given that B and C overtake A at the same instance Therefore when C overtakes A both of them have covered the same distance Let C take t hours to cover the same distance as covered by A in 8 hours

$\therefore$ 8 x 30 = t x 60 $\Rightarrow$ t = 4 hours

$\therefore$ C started after (8 - 4 = 4) hrs after A started