Time, Speed & Distance
Aptitude

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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

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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


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