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Rohan, shikha's boyfriend,had to pick her home for a live concert

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shivansh9307
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Rohan, shikha's boyfriend,had to pick her home for a live concert [#permalink] New post   24 Jul 2019, 03:32
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Rohan, Shikha's boyfriend, had to pick her from her home for a live concert on her 23rd birthday. The venue of the concert and Shikha's home were in opposite directions from Rohan's office. He got late because of some work at the office and realized that if he goes to pick Shikha from her home, which was a 48-minute drive from his office, they would be late for the show by 16 minutes. He asked her to start from her home towards his office in an auto-rickshaw and himself started driving towards her home. Both of them started simultaneously, he picked her as soon as they met and they managed to reach the venue just in time for the concert. If Rohan drives at an average speed of 60 km/hr, find the speed (in km/hr) of the auto-rickshaw.

A. 16
B. 20
c. 12
d. 15
e. None of these

Source- GMAT avengers group FB
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Re: Rohan, shikha's boyfriend,had to pick her home for a live concert [#permalink] New post   25 Jul 2019, 04:17
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shivansh9307 wrote:
Rohan, Shikha's boyfriend, had to pick her from her home for a live concert on her 23rd birthday. The venue of the concert and Shikha's home were in opposite directions from Rohan's office. He got late because of some work at the office and realized that if he goes to pick Shikha from her home, which was a 48-minute drive from his office, they would be late for the show by 16 minutes. He asked her to start from her home towards his office in an auto-rickshaw and himself started driving towards her home. Both of them started simultaneously, he picked her as soon as they met and they managed to reach the venue just in time for the concert. If Rohan drives at an average speed of 60 km/hr, find the speed (in km/hr) of the auto-rickshaw.

A. 16
B. 20
c. 12
d. 15
e. None of these

Source- GMAT avengers group FB


Rohan's speed is 60 kmph so he takes 1 min for every 1 km. Since he takes 48 min to reach Shikha, her house is 48 km away from his office.

If he goes to pick her up,

S <--------------48 km----------------- R
----------------------------------------->

he takes 96 mins to pick and reach back.
But if she also travels some distance, he takes 16 mins less.

S ===8====><---------------40------------R
==========------------------------------>

So he would not have travelled the last 8 kms to her house to and fro. So the auto would have travelled the 8 kms.
Since this is done in same time,
Ratio of Speeds = Ratio of distances

s/60 = 8/40
s = 12 kmph

Answer (C)
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Re: Rohan, shikha's boyfriend,had to pick her home for a live concert [#permalink] New post   24 Jul 2019, 06:21
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lets imagine that concert (A), Office (B), Meeting point (C), and home (D) are on a straight line:

(A)________________________(B)__________________(C)________(D)

if Rohan made a trip BD + AD, he will be 16 min late,
if Rohan made a trip BC + AC, he will be on time,
then,\(\frac{(BD + AD)}{60} - \frac{(BC + AC)}{60} = \frac{16}{60}\),
BD + AD - BC - AC = 16

if AD - AC = CD, and BD - BC = CD,
then 2CD = 16, and CD = 8km

if Home is 48 min away from Office,
then, \(\frac{BD}{60} = \frac{48}{60}\), BD = 48KM
then BC = 40km

if the time taken by Rohan to reach meeting point C is equal to time taken by Shikha to reach the same point,
then \(\frac{BC}{60} = \frac{CD}{X}\), and X = \(\frac{8*60}{40}\) = 12 km/h

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Re: Rohan, shikha's boyfriend,had to pick her home for a live concert [#permalink] New post   24 Jul 2019, 06:26
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Let the speed of the rickshaw = x.
They meet after time t

60t + xt = 60 * (48/60) = 48

16 mins saved since Shikha has traveled some distance already (while twice that distance would have to be covered had Rahul picked her up)

2d = 60 * 16/60 = 16
d= 8km

xt = 8

60t = 40, t = 2/3

Speed of Auto rickshaw = x = xt/t = 8/(2/3) = 12km/hr.

Option C.
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Re: Rohan, shikha's boyfriend,had to pick her home for a live concert [#permalink] New post   24 Jul 2019, 09:04
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shivansh9307 wrote:
Rohan, Shikha's boyfriend, had to pick her from her home for a live concert on her 23rd birthday. The venue of the concert and Shikha's home were in opposite directions from Rohan's office. He got late because of some work at the office and realized that if he goes to pick Shikha from her home, which was a 48-minute drive from his office, they would be late for the show by 16 minutes. He asked her to start from her home towards his office in an auto-rickshaw and himself started driving towards her home. Both of them started simultaneously, he picked her as soon as they met and they managed to reach the venue just in time for the concert. If Rohan drives at an average speed of 60 km/hr, find the speed (in km/hr) of the auto-rickshaw.

A. 16
B. 20
c. 12
d. 15
e. None of these

Source- GMAT avengers group FB



Shikha's home is 48 km away from Rohan's office. If he travels himself @ 60 kmh, he will be late by 16 mins
If he reduces 8 mins travel time (8 km) both sides, he will save 16 mins, and reach concert on time.
Auto has to travel 8 km in 40/60 mins
Speed of auto = 8/40*60 = 12 kmh

IMO C
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Re: Rohan, shikha's boyfriend,had to pick her home for a live concert [#permalink] New post   12 Aug 2020, 08:31
Can someone direct me to where to find more information about the source of this question? Seems like that would be helpful to prep but I personally have not heard of such an area.
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Rohan, shikha's boyfriend,had to pick her home for a live concert [#permalink] New post   19 Sep 2020, 09:19
1st scenario: R has to drive all the way to pick up S at her house


Since she lives 48 minutes away from R’s office at R’s speed of 60 km/hr:

Distance from R office to S house = 60 * (48/60)= 48 km

He must drive to her house and Tavel back in a round trip past his office for a total of 96 km + whatever distance it takes to get to the concert from R’s office.

Doing this they will be late by + 16 min


Scenario 2: R saves 16 minutes by meeting S somewhere between S’s house and R’s office


If R is able to save 16 minutes at his constant speed of 48 km/hr, then the total distance he saves is:

Distance saved by R = 48 * (16/60) = 16 km

Since R has to travel to meet S and then turn around and go past his office to get to the concert, he will save this distance across the 2 equal parts back and forth.

This means instead of traveling 48 km to S’s house, R now only has to travel:


48 - (1/2 * 16 km saved) = 40 km to the meet point where S will meet him

S must make up the extra distance and travel 8 km to the meet point.


Finally, since R leaves from his office and S leaves from her house at the SAME departure time, the time traveled will be the same/constant for both of them.


Given the Same Time traveled, the Distance each is able to travel in that same time is DIRECTLY PROPORTIONAL to their Constant Speeds


Ratio of Distance traveled to meet point between R’s Office and S’s House:


Distance-S : Distance -R = 8 : 40


Speed of S : Speed of R = X : 60


Setting up the proportion where X = Speed of S


8/40 = X/60

X = (3/2) * 8

X = 12 km/hr

Answer -C-

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Re: Rohan, shikha's boyfriend,had to pick her home for a live concert [#permalink] New post   05 Nov 2023, 06:45
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Re: Rohan, shikha's boyfriend,had to pick her home for a live concert [#permalink]
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