Arithmetic-16 (CAT-2004)

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? 

(1) 11 km/hr

(2) 12 km/hr

(3) 13 km/hr

(4) 14 km/hr

For Answer Click on "Read more" below:

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 = t₁= distance/speed = d/10 -----(1)

“If he cycles at 15 km/hr, he will arrive at the same place at 11 a.m”

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

In the second case he reaches 2 hours early, which means,

t₁ – t₂ = 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 t₃.

He has to reach 1 hour earlier when compared to the first case.

Hence, t₁- t₃ = 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)