Question

Prasoon cycled a distance of 180 km at a certain speed. if he cycled 2 km slower every hour, he would have taken 3 more hours to reach the destination. Select from the options, the speed in km/hr at which prasoon actually cycled

*Answer is (12)*

Answer 1

Let the original speed of Prasoon be s
and original time Prasoon took be t
So, we have distance = speed x time
180 = st.....(1)
Now, if he cycled 2 km slower his new speed will be = s - 2
new time taken will be = t + 3
So, we have 180 = (s - 2)(t + 3)
180 = st + 3s - 2t - 6......(2)
Solving (1) and (2) we get
180/s = t, from (1) putting this in (2) we get
180 = s(180/s) + 3s - 2(180/s) - 6
180 = 180 + 3s - 360/s - 6
3s - 360/s - 6 = 0
s - 120/s - 2 = 0
s² - 2s - 120 = 0
s² - 12s + 10s - 120 = 0
s(s - 12) + 10(s - 12) = 0
(s - 12)(s + 10) = 0
s = 12 or -10
but speed cant be negative, so s = 12
Therefore, the speed at which Prasoon actually cycled = 12 km/hr