# Time and Distance - Aptitude Questions and Answers - RejinpaulPlacement

36.
A can complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km. [Assistant Grade 1997]

Solution:   Let the total distance be x km.

Then, [(1/2)x / 21] + [(1/2)x / 24] = 10
=> x/21 + x/24 = 20
=> 15x = 168 * 20
=> x = (168 * 20) / 15 = 224 km.
37.
A person travels equal distance with speeds of 3 km/hr, 4 km/hr and 5 km/hr and takes a total time of 47 minutes. The total distance (in km) is: [R.R.B 2001]

Solution:   Let the total distance be 3x km.

Then, x/3 + x/4 + x/5 = 47/60
=> 47x/60 = 47/60.
=> x = 1.

Total distance = (3 * 1) km = 3 km.
38.
A farmer travelled a distance of 61 km in 9 hours. He travelled partly on foot @ 4 km/hr and partly on bicycle @ 9 km/hr. The distance travelled on foot is: [U.P.S.C 2002]

Solution:   Let the distance travelled on foot be x km.

Then, distance travelled on bicycle = (61 - x) km.
So, x/4 + (61 - x)/9 - 9
<=> 9x + 4 (61 - x) = 9 * 36
<=> 5x = 80
<=> x = 16 km.
39.
A is faster than B. A and B each walk 24 km. The sum of their speeds is 7 km/hr and the sum of times taken by them is 144 hours. Then, A s speed is equal to: [I.A.F. 2002]

Solution:   Let A s speed = x km/hr.

Then, B s speed = (7 - x) km/hr.

So, (24/x) + 24/(7 - x) = 14
=> 24 (7 - x) + 24x = 14x (7 - x)
=> 14 x^2 - 98x + 168 = 0
=> x^2 - 7x + 12 = 0
=> (x - 3) (x - 4) = 0
=> x = 3 or x = 4

Since A is faster than B.
So, A s speed = 4 km/hr
B s speed = 3 km/hr.
40.
A person travels from P to Q at a speed of 40 kmph and returns by increasing his speed by 50%. What is his average speed for both the trips? [M.B.A 2003]

Solution:   Speed on return trip = 150% of 40 = 60 kmph.

Average speed = (2 * 40 * 60) / (40 + 60) km/hr
= (4800/100) km/hr
= 48 km/hr.
41.
A car driver travels from the plains to the hill station, which are 200 km apart at an average speed of 40 km/hr. In the return trip, he covers the same distance at an average speed of 20 km/hr. The average speed of the car over the entire distance of 400 km is:

Solution:   Average speed = (2 * 40 * 20) / (40 + 60) km/hr
= (80/3) km/hr = 26.67 km/hr
42.
Mac travels from A to B a distance of 250 miles in 5   1/2 hours. He returns to A in 4 hours 30 minutes. His average speed is: