Arithmetic-13 (XAT-2009)

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 follows here:

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 = t₁= distance/speed = d/10 -----(1)

“If he walks at 15 km an hour, he returns to home at 18.30 hours”

t₂= distance/speed = d/15                           ----- (2)

In the second case he reaches half-an-hour early to home, which means,

t₁ – t₂ = 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 t₃.

He has to reach 15 minutes earlier when compared to the second case.

Hence, t₂- t₃ = 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)