Question

Sebastian and his father went on a driving trip. They want to refuel the car and want to change tyres of the car in minimum time. Gas stations are located at an interval of 40 miles and mechanic shops are located at an interval of 30 miles from their house in same direction.

Find the minimum distance at which both the gas station and mechanic shop can be located at the same stop.

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Solution

The correct option is **B** 120 miles

As both the gas station and mechanic shop needs to be located at the same stop, the distance of the stop should be a multiple of both 40 miles and 30 miles

For minimum distance, we need to find the LCM.

40=23×5

30=2×3×5

∴ LCM =23×3×5=120

(by excluding any repetitive prime factors from both the numbers)

Hence, the required distance is 120 miles.

As both the gas station and mechanic shop needs to be located at the same stop, the distance of the stop should be a multiple of both 40 miles and 30 miles

For minimum distance, we need to find the LCM.

40=23×5

30=2×3×5

∴ LCM =23×3×5=120

(by excluding any repetitive prime factors from both the numbers)

Hence, the required distance is 120 miles.

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