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26 Nov 2024, 01:30
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B
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Difficulty:
95%
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Question Stats:
39% (01:40) correct
61%
(01:40)
wrong
based on 192
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Prem and Ramesh started from two cities Patna and Allahabad respectively, traveling at constant speeds, to reach Allahabad and Patna respectively. At what time will they meet?
(1) The distance between Patna and Allahabad is 250 km. Prem travels at 50 km/hr and Ramesh travels at 25 km/hr
(2) Prem started from Patna at 5:00 a.m. and reached Allahabad at 11:00 a.m. Ramesh started from Allahabad at 7:00 a.m. and reached Patna at 3.00 p.m.
(1) The distance between Patna and Allahabad is 250 km. Prem travels at 50 km/hr and Ramesh travels at 25 km/hr
(2) Prem started from Patna at 5:00 a.m. and reached Allahabad at 11:00 a.m. Ramesh started from Allahabad at 7:00 a.m. and reached Patna at 3.00 p.m.
26 Nov 2024, 05:43
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IMHO C is the correct answer.
Statement 1: The distance between Patna and Allahabad is 250km. Prem travels at 50 km.h, and Ramesh travels at 25 km/h.
Relative speed when traveling towards each other is: 50 + 25 = 75 km/h;
Time to meet = Distance/Relative speed = 250/75 = 10/3 hours (3 hours and 20 min);
However, this calculation assumes both started at the same time, which is not stated. Without knowing the starting times, Statement 1 alone is insufficient.
Statement 2: Prem started at 5:00 am from Patna and reached Allahabad at 11:00 am. Ramesh started at 7:00 am and reached Patna at 3:00 pm.
From this, we can calculate the speeds:
Prem's travel time: 5 am to 11 am, which is 6 hours. Therefore, 250 km/6 hours = 41.6 km/h;
Ramesh's travel time 7 am to 3 pm, which is 8 hours. Therefore, 250 km/8 hours = 31.2 km/h;
However, we don't know their meeting time because we don't know how far each traveled before meeting. So, Statement 2 alone is insufficient.
Using the speeds from Statement 1 and starting times from Statement 2:
Prem starts at 5 am, and Ramesh starts at 7 am, giving Prem a 2-hour head start. In 2 hours, Prem travels 50 km/h * 2 hours = 100 km. So, at 7 am Prem is 100 km away from Patna;
At 7 am, the distance between them is 250 - 100 = 150 km;
They are now traveling towards each other at a relative speed of 50 + 25 = 75 km/h;
Time to meet: 150/75 = 2 hours. Therefore, they meet at 7 am + 2 hours = 9:00 am. Hence, both statements together are sufficient to answer the question, but neither alone is sufficient.
Statement 1: The distance between Patna and Allahabad is 250km. Prem travels at 50 km.h, and Ramesh travels at 25 km/h.
Relative speed when traveling towards each other is: 50 + 25 = 75 km/h;
Time to meet = Distance/Relative speed = 250/75 = 10/3 hours (3 hours and 20 min);
However, this calculation assumes both started at the same time, which is not stated. Without knowing the starting times, Statement 1 alone is insufficient.
Statement 2: Prem started at 5:00 am from Patna and reached Allahabad at 11:00 am. Ramesh started at 7:00 am and reached Patna at 3:00 pm.
From this, we can calculate the speeds:
Prem's travel time: 5 am to 11 am, which is 6 hours. Therefore, 250 km/6 hours = 41.6 km/h;
Ramesh's travel time 7 am to 3 pm, which is 8 hours. Therefore, 250 km/8 hours = 31.2 km/h;
However, we don't know their meeting time because we don't know how far each traveled before meeting. So, Statement 2 alone is insufficient.
Using the speeds from Statement 1 and starting times from Statement 2:
Prem starts at 5 am, and Ramesh starts at 7 am, giving Prem a 2-hour head start. In 2 hours, Prem travels 50 km/h * 2 hours = 100 km. So, at 7 am Prem is 100 km away from Patna;
At 7 am, the distance between them is 250 - 100 = 150 km;
They are now traveling towards each other at a relative speed of 50 + 25 = 75 km/h;
Time to meet: 150/75 = 2 hours. Therefore, they meet at 7 am + 2 hours = 9:00 am. Hence, both statements together are sufficient to answer the question, but neither alone is sufficient.
IMO the answer is B.
Statement 1 is insufficient as no time is mentioned.
Statement 2
Suppose, total distance = d
Prem's total time = 6 hours
Prem's speed = \(\frac{d}{6}\)
Ramesh's total = 8 hours
Ramesh's speed = \(\frac{d}{8}\)
Prem got a headstart and continued for 2 hours until Ramesh started. In those 2 hours Prem crossed -
= \(\frac{d}{6} * 2\)
= \(\frac{d}{3}\) km
Now when Ramesh joined, the relative speed stands \(= \frac{d}{6}+\frac{d}{8} = \frac{16d}{60} = \frac{7d}{24}\)
Relative time = \(\frac{Distance }{ Relative Speed}\\
= \frac{Total Distance - Distance Prem Crossed Before Ramesh Started}{Relative Speed}\\
= (d-d/3) / \frac{7d}{24}\\
= \frac{2d}{3}*\frac{24}{7d}\\
= 16/7 hours\)
Now total time passed when they met, since Prem started
= time taken by Prem before Ramesh started + when they met after Ramesh started
= 2 hours + 16/7 Hours
= 4 hours 18 min approx
They'll meet at = 5:00 AM + 4 hours 18 min = 9:18 AM approx.
So statement 2 is sufficient.
ANSWER B
Statement 1 is insufficient as no time is mentioned.
Statement 2
Suppose, total distance = d
Prem's total time = 6 hours
Prem's speed = \(\frac{d}{6}\)
Ramesh's total = 8 hours
Ramesh's speed = \(\frac{d}{8}\)
Prem got a headstart and continued for 2 hours until Ramesh started. In those 2 hours Prem crossed -
= \(\frac{d}{6} * 2\)
= \(\frac{d}{3}\) km
Now when Ramesh joined, the relative speed stands \(= \frac{d}{6}+\frac{d}{8} = \frac{16d}{60} = \frac{7d}{24}\)
Relative time = \(\frac{Distance }{ Relative Speed}\\
= \frac{Total Distance - Distance Prem Crossed Before Ramesh Started}{Relative Speed}\\
= (d-d/3) / \frac{7d}{24}\\
= \frac{2d}{3}*\frac{24}{7d}\\
= 16/7 hours\)
Now total time passed when they met, since Prem started
= time taken by Prem before Ramesh started + when they met after Ramesh started
= 2 hours + 16/7 Hours
= 4 hours 18 min approx
They'll meet at = 5:00 AM + 4 hours 18 min = 9:18 AM approx.
So statement 2 is sufficient.
ANSWER B
