If a man cycles at 10
km/hr, he arrives at a certain place at 1 p.m. If he cycles at 15 km/hr, he will
arrive at the same place at 11 a.m. At what speed must he cycle to get there at
noon?

Solution:

(1) 11 km/hr

(2) 12 km/hr

(3) 13 km/hr

(4) 14 km/hr

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Solution:

Let the
total distance be d.

“If
a man cycles at 10 km/hr, he arrives at a certain place at 1 p.m”

Speed =
distance/time => time = t

_{1}= distance/speed = d/10 -----(1)
“If
he cycles at 15 km/hr, he will arrive at the same place at 11 a.m”

t

_{2}= distance/speed = d/15 ----- (2)
In the
second case he reaches 2 hours early, which means,

t

_{1}– t_{2}= 2 => d/10 – d/15 = 2 => d((15-10)/(10*15)) = 2 => d/30 = 2 => d=60 km
“At
what speed must he cycle to get there at noon ie., 12’O clock”

In this
case let his speed be x and time taken be t

_{3}.
He has
to reach 1 hour earlier when compared to the first case.

Hence,
t

_{1}- t_{3 }= 1 hour => d/10 – d/x = 1 => 60/10 – 60/x = 1
=> 60/x
= 6-1 = 5 => x = 60/5 = 12

Hence
his speed must be 12 kmph in order to reach at noon

**Answer (2)**
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