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Question

# A man cycles to his office from his house at a speed of 5 km/h and reaches 10 minutes late. If he cycles at a speed of 6 km/h, he reaches 10 minutes early. What is the distance between the office and his house?

A
40 km
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B
20 km
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C
35 km
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D
10 km
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Solution

## The correct option is D 10 kmLet the distance between the office and his house is x km and 't hr' be the normal time taken. Cycling from House to office:Speed = 5 km/h and time taken = (t+1060)hourSo, distance = 5(t+1060)km ... (1)Cycling from Office to house:Speed = 6 km/h and time taken = (t−1060)hourSo, distance = 6(t−1060)km ...(2)From (1) and (2), we get5(t+1060)=6(t−1060)⟹5(t+16)=6(t−16)⟹5(6t+1)=6(6t−1)⟹30t+5=36t−6⟹30t−36t=−6−5⟹−6t=−11⟹t=116hourPut value of t=116hour in (1), we getDistance = 5(116+1060)=5(116+16)=5(126)=10kmHence, the distance between his house and office is 10 km.

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