A person has to travel from point A to point B in car in a scheduled time at uniform speed Due to so...........

Quantitative Aptitude ( CCS) Time & distance

A person has to travel from point A to point B in car in a scheduled time at uniform speed. Due to some problem in car engine, the speed of car has to be decreased by 1/5th of the original speed after covering 30 km. With this speed he reaches point B 45 minutes late than the scheduled time. Had the engine be malfunctioned after 48 km, he would have reached late by only 36 minutes. Find the distance between points A and B.

120 km

80 km

100 km

150 km

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Explanation:

Solution:
Let total distance be d km, speed = u, and time = t hours
So case 1:
30 km with speed u, (d-30) with speed 1 – 1/5 = 4/5 of u
If he would have travelled (d-30) by speed u, then time = (d-30)/u
But now time is = (d-30)/(4u/5) = 5(d-30)/4u
And difference in timings is 45 minutes = 3/4 hour
So 5(d-30)/4u – (d-30)/u = 3/4
Solve (d-30)/u = 3
case 2:
48 km with speed u, (d-48) with speed 1 – 1/5 = 4/5 of u
If he would have travelled (d-48) by speed u, then time = (d-48)/u
But now time is = (d-48)/(4u/5) = 5(d-48)/4u
And difference in timings is 36 minutes = 3/5 hour
So 5(d-48)/4u – (d-48)/u = 3/5
Solve (d-48)/4u = 3/5
Divide both equations, d = 120 km