Time, Speed & Distance
Aptitude

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Q.

Vikas can cover a distance in 1 hr 24 min by covering (left(dfrac{2}{3}right)^{rd})of the distance at 4 kmph and the rest at 5kmph. The total distance is?

 A.

4 km

 B.

6 km

 C.

8 km

 D.

10 km

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Solution:
Option(B) is correct

Let total distance be $S$

total time = 1 hr 24 min = 84 min

\(\dfrac{84}{60}=\dfrac{21}{15}\) hr

Let Vikas travels from $A->T->S$

A ------------------------ T ------------ S

<---------- \(\left(\dfrac{2S}{3}\right)\)---------><----\(\left(\dfrac{S}{3}\right)\)---->

$A$ to $T$ :: speed = 4 kmph

Distance = \(\left(\dfrac{2}{3}\right)\times S\)

T to S :: speed = 5 km = 

Distance = \(\left(1-\dfrac{2}{3}\right)S=\dfrac{1}{3}S\)

Total time:

\(\dfrac{21}{15}=\dfrac{2/3S}{4}+\dfrac{1/3S}{4}\)

$84=10S+4S$ {Multiply both sides by $15\times 4$}

\(S=\dfrac{84}{14}=6\) km


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