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Question

# Ravi starts for his school at 8:20 am on his bicycle. If he travels at a speed of 10 km/h then he reaches his school late by 8 minutes but on travelling at 16 km/h, he reaches the school 10 minutes early. At what time does the school start?

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Solution

## Let the total distance = x km Let the time taken by Ravi to reach the school at sharp time = l min. If the speed of the bicycle is 10 km/ h then he reaches his school late by 8 min. ∴x10=l+860 ⇒x10=l+215 ...(i) If the speed of the bicycle is 16 km/ h then he reeach his school 10 min early. ∴x16=l−1060⇒x16=l−16 ...(ii) On solving Eqs. (i) and (ii), we get, x10−x16=215+16⇒8x−5x80=4+530⇒3x80=930⇒x=9×8030×3=8 km Now, put x=8 in Eq.(i) ,we get 810=t+215⇒t=810−215=24−430⇒t=2030=23h=23×60=40 min So the time of school is 9:00 am.

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