A car travels from P to Q at a constant speed If its speed were increased by 10 km hr it would have ...........

Quant (SSC) Time & distance

A car travels from P to Q at a constant speed. If its speed were increased by 10 km/hr, it would have been taken one hour lesser to cover the distance. It would have taken further 45 minutes lesser if the speed were further increased by 10 km/hr. The distance between the two cities is

540 km

420 km

600 km

620 km

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Explanation:

Product of Speeds = Distance × Diff. in Speeds / Diff. in time
Let initial speed be x km/hr and the distance between P and Q be D.
In the 1^st scenario,
Initial speed = x, Increased speed = (x + 10), difference in speeds
= 10 kmph and difference in time = 1 hr
x(x + 10) = D x 10 /1 ,,,,,,,i
In the 2nd scenario,
Initial speed = x, Increased speed = (x + 20), difference in speeds = 20 kmph and difference in time
= 1 hr + 45 min = 1+ 3/4 = 7/4 hrs.
x(x + 20) = D × 20 × 4 /7 ............ii
Dividing Eq. (ii) by Eq.(i) , we get
(x + 20) /(x + 10) = 20 x 4 /7 x 1/10 = 8/7
⇒ 140 + 7x = 80 + 8x
∴ x = initial speed = 60 km/hr
Putting the value of x in eq. (i), we get
60 × 70 = D × 10
∴ D = 420 km.