A worker reaches his factory 3 minutes late if his speed from his house to the factory is 5 km/hr. If he walks at a speed of 6 km/hr, then he reaches the factory 7 minutes early. The distance of the factory from his house is

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Q: 140 (IAS/2001)
A worker reaches his factory 3 minutes late if his speed from his house to the factory is 5 km/hr. If he walks at a speed of 6 km/hr, then he reaches the factory 7 minutes early. The distance of the factory from his house is

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,0,7,1,0,5,1

keywords: 

{'distance': [0, 3, 3, 3], 'speed': [0, 1, 2, 0], 'minutes': [0, 0, 1, 1], 'km': [0, 0, 2, 1], 'worker': [0, 0, 1, 2], 'factory': [1, 0, 3, 4], 'hr': [0, 1, 2, 1]}

The question asks for the distance between the worker`s house and his factory.

Option 1: If the distance were 4 km, the worker would reach the factory in 48 minutes at a speed of 5 km/hr and in 40 minutes at a speed of 6 km/hr. This doesn`t meet the late-early conditions given in the problem, so it`s incorrect.

Option 2: If the distance were 5 km, the worker would reach the factory in 60 minutes at a speed of 5 km/hr and in 50 minutes at a speed of 6 km/hr. According to the problem, he would be 3 minutes late with the first speed and 7 minutes early with the second speed, which adds up to a 60 minute journey. This meets the condition given, so it`s correct.

Option 3: If the distance were 6 km, the worker would reach the factory in 72 minutes at a speed of 5 km/hr and in 60 minutes at a speed of 6 km/hr. This doesn`t meet the late-early conditions given in the problem, so it`s incorrect.

Option 4: If the distance were 7 km, the worker would reach the factory in 84 minutes at a