Q. 1
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
A cyclist covers half as much distance again as a tanga, driver and the tanga driver half as much again as a man on foot. If a man can walk a distance of 3 miles in an hour, how long will it take the cyclist to cover a distance of 27 miles?
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Step-by-Step Explanation & Concept Rationale
The phrase "half as much distance again" means 1.5 times the speed or distance of the baseline person.
Find the speed of the man on foot:
Given, the man walks 3 miles per hour.
Find the speed of the tanga driver:
He goes 1.5 times faster than the man.
\(\text{Speed} = 3 \times 1.5 = \mathbf{4.5\text{ miles/hour}}\)
Find the speed of the cyclist:
He goes 1.5 times faster than the tanga driver.
\(\text{Speed} = 4.5 \times 1.5 = \mathbf{6.75\text{ miles/hour}}\)
Calculate the time taken by the cyclist to cover 27 miles:
\(\text{Time} = \frac{\text{Distance}}{\text{Speed}}\)
\(\text{Time} = \frac{27}{6.75} = \mathbf{4\text{ hours}}\)
Find the speed of the man on foot:
Given, the man walks 3 miles per hour.
Find the speed of the tanga driver:
He goes 1.5 times faster than the man.
\(\text{Speed} = 3 \times 1.5 = \mathbf{4.5\text{ miles/hour}}\)
Find the speed of the cyclist:
He goes 1.5 times faster than the tanga driver.
\(\text{Speed} = 4.5 \times 1.5 = \mathbf{6.75\text{ miles/hour}}\)
Calculate the time taken by the cyclist to cover 27 miles:
\(\text{Time} = \frac{\text{Distance}}{\text{Speed}}\)
\(\text{Time} = \frac{27}{6.75} = \mathbf{4\text{ hours}}\)
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