Question

A bus covers a certain distance with uniform speed. If the speed of the bus would have been increased by 15 km/h, it would have taken two hours less to cover the same distance. And if the speed of the bus would have been decreased by 5 km/h, it would have taken one hour more to cover the same distance. Find the distance kilometres covered by the bus.

• A. 300
• B. 350
• C. 360
• D. 600

Answer 1

The correct option is C 360

Let the distance covered be d.
Let the usual speed of the bus be s and usual time taken be t
(s+15)(t-2) = d ...(i)
(s-5)(t+1) = d....(ii)
st = d....(iii)
Therefore,
From (i) and (ii)
(s+ 15)(t - 2) = (s - 5)(t + 1)
st - 2s + 15t - 30 = st + s - 5t - 5
20t - 25 = 3s....(iv)
From (i) and (iii)
(s+15)(t-2) = st
st - 2s - 30 + 15t = st
2s - 15t + 30 = 0....(v)
Now, equate the time 't' from (iv) and (v)
$\frac{3s+25}{20}=\frac{2s+30}{15}$
45s + 375 = 40s + 600
5s = 225
s = 45
Thus, t = $\frac{3\times 45+25}{20}$ = 8 hr
Thus, distance= $45\times 8$ = 360 km