75 km/h = 75*1000/3600 = 20.8 m/s

t1 = 1000/20.8 = 48s
t2 = 48+2 = 50

v2 = s/t2 = 1000/50 = 20 m/s = 72 km/h

(b)

We know speed = distance/time

STEP 1
given to us speed = 75km/hr
distance = 1km
calculate the time = 1/75 = 1/75*3600 = 48sec
Now at the certain constant speed (x) to cover 1 km time taken is 50sec(48+2 sec)

STEP 2
distance = 1km time =50 sec
sped = d/t = 1*1000/50 = 20meters/sec
convert it to km/hr = 20/1000*3600 = 72km/hr (B)

or

AFTER STEP 1
lets try substituting the values from answer choices, we will start with B & D as values are in increasing order

For (D) 1km/73km/hr = 1*3600/73 = 49.31sec, value very close to 50 sec so in order to get the right value we need to reduce the denominator value.
Now check for (B).
1km/72km/hr = 1*3600/72 = 50 secs, thats what our value is from Step 1 hence (B)

pardeep_10sharma wrote:A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 75 kilometers per hour. At what speed, in kilometers per hour, is the car traveling?
A. 71.5
B. 72
C. 72.5
D. 73
E. 73.5

time for traveling 1 Km @ 75kmph = 60 * 60 / 75 = 48 secs.

at normal speed it takes 2 secs more OR a %increase of 2/48 =1/24

which is equivalent to a 1/25th decrease in the speed or speed is 24/25 * 75 = 72 Kmph.

r = rate
t= time in hours
1 km= r(t+2/3600)
1 km= 75 km/hr *t
t= 1/75 hr
replace t into first equation and solve for r
r= 72 km/hr

Thanks to all for such wonderful replies. I was making as illy mastake. Thanks to make me realize that.