# Moderate Time, Speed & Distance Solved QuestionAptitude Discussion

 Q. A bus overtakes two boys who are walking in the direction of the bus at 2 km/hr and 4 km/hr in 9 sec and 10 sec respectively. The length of the bus and its speed are:
 ✔ A. $50$ m and $\dfrac{55}{9}$ m/s ✖ B. $80$ m and $\dfrac{88}{9}$ m/s ✖ C. $70$ m and $\dfrac{77}{9}$ m/s ✖ D. $60$ m and $\dfrac{66}{9}$ m/s

Solution:
Option(A) is correct

$a$ = length of the bus ,

$b$ = speed of the bus in m/s

Relative speed with respect to first one:

$=b-\dfrac{5}{9}=\dfrac{9b-5}{9}$

(As, 2 kmph $=\dfrac{5}{9}$ m/s)

$\Rightarrow \dfrac{a}{\left(\dfrac{9b-5}{9}\right)}=9$

$\Rightarrow a=9b-5$--------(i)

Similarly for second one:

$\Rightarrow \dfrac{a}{\left(\dfrac{9b-10}{9}\right)}=10$

$\Rightarrow 90b-9a=100$--------(ii)

From Eq (i) and (ii):

$a$ = 50 m and $b$ = 50/9 m/s