A man goes from home to office at an average speed of a km/hr. and on

Question

A man goes from home to office at an average speed of a km/hr. and on reaching office he realizes that he forgot his phone charger on his table at home. So, he immediately travels back to home at speed of b km/hr and reaches home. He maintained an average speed of c km/hr during his complete travel from home to office and then from office to home. is a≤10?

1) a ≤ b
2) c = 20 km/hr.

Source: https://www.GMATinsight.com

chetan2u · Answer

Distance is same, say d, when the speed is a and b. The average speed is c while traveling twice the distance or 2d.

The time taken has to be same =>  \frac{d}{a}+\frac{d}{b}=\frac{2d}{c} 
 \frac{1}{a}+\frac{1}{b}=\frac{2}{c}

1) a ≤ b
we do not know the value of any of the variable.
Insuff

2) c = 20 km/hr.
 \frac{1}{a}+\frac{1}{b}=\frac{2}{20}=\frac{1}{10} 
As none of a and b are 0 or negative, they have to be greater than 10 to get the right side as 1/10.
Suff. a>10

B

gurmukh · Answer

First statement is not sufficient in itself.
From second statement
C= (2ab)÷ (a+b)
10= ab÷ (a+b)
b =10a÷(a-10)
As a and b are positive so a has to be greater then 10.

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QuantMadeEasy · Answer

Understanding of the concept 
Average speed formula is total distance/Total Time.
Also, Average speed is always closer to the slower speed.
 
No information about values of a and b, hence Insufficient
 
Lets understand and apply meaning of average speed, when a=10 and b=30, exact mid point is 20.
According to the question average speed is 20, as already mentioned average speed is closed to the slower speed, therefore a must be greater than 10. Sufficient
No calculation required, but only understanding of the concept.
B is correct.

Archit3110 · Answer

Let distance a to b be x
So total distance 2x
Time for atob x/a and b to a x/b
Total time x*a+b/ab
Avg speed of complete trip
2x*ab/x*(a+b) =c
2ab/a+b=c
#1 a<=b
Insufficient 
#2 c =20
Or say
ab/a+b =10
Avg speed is 10
So a should a be >10 
Option B

ShankSouljaBoi · Answer

How did you move forward from the highlighted part... Have you used GM >=HM ???

ShankSouljaBoi · Answer

How did you arrive at this . Nowehere it is mentioned that a > b or a < = b

Best !

bumpbot · Answer

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A man goes from home to office at an average speed of a km/hr. and on

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