Rajesh
walks to and fro to a shopping mall. He spends 30 minutes in shopping. If he
walks at a speed of 10 km an hour, he returns to home at 19.00 hours. If he
walks at 15 km an hour, he returns to home at 18.30 hours. How fast must he
walk in order to return home at 18.15 hours?

A. 17 km/hour

B.
17.5 km/hour

C.
18 km/hour

D. 19 km/hour

E. None of these**Solution:**

Let the total distance be d.

“If he walks at a speed of 10 km an
hour, he returns to home at 19.00 hours”

Speed = distance/time => time = t

_{1}= distance/speed = d/10 -----(1)
“If he walks at 15 km an hour, he returns
to home at 18.30 hours”

t

_{2}= distance/speed = d/15 ----- (2)
In the second case he reaches
half-an-hour early to home, which means,

t

_{1}– t_{2}= ½ => d/10 – d/15 = ½ => d((15-10)/(10*15)) = ½ => d/30 = ½ => d=15 km
“How fast must he walk in order to return
home at 18.15 hours”

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

_{3}.
He has to reach 15 minutes earlier
when compared to the second case.

Hence, t

_{2}- t_{3 }= 15 minutes = ¼ hour => d/15 – d/x = ¼ => 15/15 – 15/x = ¼
=> 15/x = 1-(1/4) = ¾ => x =
4*15/3 = 20

Hence his speed must be 20 kmph in
order to reach home at 16.15hours

**Answer (E)**

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