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JayPatadiya
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Pankaj started walking from point A to point B and Prakash s 22 Dec 2019, 03:04
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Difficulty:

95% (hard)

Question Stats:

47% (03:08) correct 53% (03:37) wrong based on 106 sessions

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Pankaj started walking from point A to point B and Prakash started walking from point B to point A, both started at 6:00 AM. After walking for 2 hours, both met each other and sat down for breakfast, which took 1 hour. Then both continued their journey. Since they just had their brakfast, their speed reduced to half of their original speed. After one hour, Prakash realized that their keys got exchanged, so he started running towards Pankaj at two and a half times his present speed. If the ratio of Pankaj's and Prakash's original speed was 3:2, at what time would Prakash and Panakj meet to exchange their keys?

A.12:00 PM
B.12:30 PM
C.01:00 PM
D.01:30 PM
E.11:30 AM

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nick1816
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Pankaj started walking from point A to point B and Prakash s 22 Dec 2019, 03:52
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The ratio of their speed will remain 3:2 after the breakfast.

Speed of Pankaj= 3v
Speed of Parkash= 2v

Distance between them after 1 hour = 3v+2v=5v

Speed of Parkash after one hour= 2.5*2v=5v

Their relative speed= 5v-3v=2v

Time taken by Parkash to reach Pankaj again= 5v/2v=2.5 hours

They will meet second time at (6+2+1+1+2.5)= 12:30 PM


JayPatadiya
Pankaj started walking from point A to point B and Prakash started walking from point B to point A, both started at 6:00 AM. After walking for 2 hours, both met each other and sat down for breakfast, which took 1 hour. Then both continued their journey. Since they just had their brakfast, their speed reduced to half of their original speed. After one hour, Prakash realized that their keys got exchanged, so he started running towards Pankaj at two and a half times his present speed. If the ratio of Pankaj's and Prakash's original speed was 3:2, at what time would Prakash and Panakj meet to exchange their keys?

A.12:00 PM
B.12:30 PM
C.01:00 PM
D.01:30 PM
E.11:30 AM

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Pankaj started walking from point A to point B and Prakash s 22 Dec 2019, 06:52
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JayPatadiya
Pankaj started walking from point A to point B and Prakash started walking from point B to point A, both started at 6:00 AM. After walking for 2 hours, both met each other and sat down for breakfast, which took 1 hour. Then both continued their journey. Since they just had their brakfast, their speed reduced to half of their original speed. After one hour, Prakash realized that their keys got exchanged, so he started running towards Pankaj at two and a half times his present speed. If the ratio of Pankaj's and Prakash's original speed was 3:2, at what time would Prakash and Panakj meet to exchange their keys?

A.12:00 PM
B.12:30 PM
C.01:00 PM
D.01:30 PM
E.11:30 AM
Show more

6am-8am:
Let Pankaj's rate = 6 miles per hour and Prakash's rate = 4 miles per hour, with the result that their rate ratio = 6:4 = 3:2.

8am-9am:
Breakfast

9am-10am:
Pankaj's rate decreases by 50% to 3 miles per hour.
Prakash's rate decreases by 50% to 2 miles per hour.
When Pankaj and Prakash travel away from each other, they WORK TOGETHER to increase the distance between them.
When people work together, ADD THEIR RATES.
New combined rate for Pankaj and Prakash = 3+2 = 5 miles per hour.
Since their combined rate = 5 miles per hour, the distance between them after 1 hour = r*t = 5*1 = 5 miles.

10am - key exchange:
Prakash's increased rate = 2.5 times his post-breakfast rate of 2 miles per hour = 5 miles per hour.
Since Prakash and Pankaj are separated by 5 miles, Prakash must CATCH UP by 5 miles to perform the key exchange.
The CATCH-UP rate is the DIFFERENCE between Prakash's increased rate and Pankaj's post-breakfast rate:
5-3 = 2 miles per hour.
Since Prakash must catch up by 5 miles at a catch-up rate of 2 miles per hour, the time to catch up \(= \frac{d}{r} = \frac{5}{2} = 2.5\) hours.
Thus:
Time of the key exchange = 10am + 2.5 hours = 12:30pm.

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Pankaj started walking from point A to point B and Prakash s 08 May 2020, 06:08
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JayPatadiya
Pankaj started walking from point A to point B and Prakash started walking from point B to point A, both started at 6:00 AM. After walking for 2 hours, both met each other and sat down for breakfast, which took 1 hour. Then both continued their journey. Since they just had their brakfast, their speed reduced to half of their original speed. After one hour, Prakash realized that their keys got exchanged, so he started running towards Pankaj at two and a half times his present speed. If the ratio of Pankaj's and Prakash's original speed was 3:2, at what time would Prakash and Panakj meet to exchange their keys?

A.12:00 PM
B.12:30 PM
C.01:00 PM
D.01:30 PM
E.11:30 AM

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j/k=3/2, j/k=3x/2x

distance k returns to get key: distance k traveled + distance j traveled
... 2x/2*1+3x/2*1 = 5x/2 = 2.5x

time k meets to get keys: distance apart / dif rates
.. 2.5x/[2.5(2x/2)-(3x/2)]=5x/2x=2.5 hrs

time they meet: 2hr + 1hr (brk) + 1hr (oppos) + 2.5hr (key)
.. 4+2.5=6.5; they began 06:00+6:30=12:30

ans (B)
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Pankaj started walking from point A to point B and Prakash s 31 Jul 2025, 03:24
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GMATGuruNY
JayPatadiya
Pankaj started walking from point A to point B and Prakash started walking from point B to point A, both started at 6:00 AM. After walking for 2 hours, both met each other and sat down for breakfast, which took 1 hour. Then both continued their journey. Since they just had their brakfast, their speed reduced to half of their original speed. After one hour, Prakash realized that their keys got exchanged, so he started running towards Pankaj at two and a half times his present speed. If the ratio of Pankaj's and Prakash's original speed was 3:2, at what time would Prakash and Panakj meet to exchange their keys?

A.12:00 PM
B.12:30 PM
C.01:00 PM
D.01:30 PM
E.11:30 AM

6am-8am:
Let Pankaj's rate = 6 miles per hour and Prakash's rate = 4 miles per hour, with the result that their rate ratio = 6:4 = 3:2.

8am-9am:
Breakfast

9am-10am:
Pankaj's rate decreases by 50% to 3 miles per hour.
Prakash's rate decreases by 50% to 2 miles per hour.
When Pankaj and Prakash travel away from each other, they WORK TOGETHER to increase the distance between them.
When people work together, ADD THEIR RATES.
New combined rate for Pankaj and Prakash = 3+2 = 5 miles per hour.
Since their combined rate = 5 miles per hour, the distance between them after 1 hour = r*t = 5*1 = 5 miles.

10am - key exchange:
Prakash's increased rate = 2.5 times his post-breakfast rate of 2 miles per hour = 5 miles per hour.
Since Prakash and Pankaj are separated by 5 miles, Prakash must CATCH UP by 5 miles to perform the key exchange.
The CATCH-UP rate is the DIFFERENCE between Prakash's increased rate and Pankaj's post-breakfast rate:
5-3 = 2 miles per hour.
Since Prakash must catch up by 5 miles at a catch-up rate of 2 miles per hour, the time to catch up \(= \frac{d}{r} = \frac{5}{2} = 2.5\) hours.
Thus:
Time of the key exchange = 10am + 2.5 hours = 12:30pm.

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My answer for this question is 12:00PM, and when I read all the answers, I still don't feel satisfied.

I see 1 flaw in the question and the answer: "Pankaj started walking from point A to point B", so according to the question, Pankaj's journey will end at B - NO COMING BACK, NO KEEP MOVING

"Let Pankaj's rate = 6 miles per hour and Prakash's rate = 4 miles per hour", so the distance between A and B is: (6 + 4) * 2 = 20 miles

They met after 2 hours, so the meeting point is 12 miles from A, which means Pankaj has an 8-mile journey left.

After breakfast (9 AM), Pankaj kept going toward B at a new speed: 3 miles per hour, so he would arrive at B in 9 + 8/3 = 11:40 AM and stay there - NO COMING BACK, NO KEEP MOVING from the logic above.

After breakfast (9 AM), Prakash kept going toward A at a new speed: 2 miles per hour. When he found out he kept the wrong key (10 AM), his position was 8 + 2 = 10 miles from B. Then he ran toward B at a new speed: 2 * 2,5 = 5 miles per hour, which took: 10/5 = 2 hours. So he will arrive at B at 10 + 2 = 12:00 PM, where he met Pankaj, who had already arrived at B at 11:40 AM.

So the answer should be 12:00 PM

The answer 12:30 PM is only right if the question mentions Pankaj'll keep moving in the same direction after arriving at B (away from B)
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