Q.1.What is the distance between Alankar’s house and office, if he will reach office late by 20 minutes, traveling at 10 km/hr and will reach early by 15 minutes, traveling at 15 km/hr?

a) 14.5 km

b) 17.5 km

c) 16.5 km

d) 15 km

Sol : Option B Explanation: : Difference in timing = 15 – (–20) = 35 min. Let required distance = x.
∴ x/10 - x15 = 35/60 → x = 17.5 km.

Q.2. What is the average speed if a man drives 3 hours at 60 km/hr and the next 6 hours at 50 km/hr.?

a) 55 km/hr

b) 52.5 km/hr

c) 53.33 km/hr

d) 56.67 km/hr

Sol : Option C Explanation: Average speed =
Total distance/Total time → [(3x60)+(6x50)]/(3+6) = 480/9
=53.33 km/hr

Q.3. A train without stoppages travels at the rate of 50 km per hour and with stoppages travels at the rate of 45 km an hour. How many minutes does the train stop on an average per hour?

a) 6 min

b) 10 min

c) 5 min

d) 8 min

Sol : Option A Explanation: Minutes/hr the train stops = (50 -45)/50 x 60 = 5/60 x 60 → 6 min.

Q.4.Two cyclists do the same journey by travelling at 9 km/hr and 10 km/hr respectively. Find the distance travelled when one takes 32 minutes longer than the other.

a) 44 km

b) 48 km

c) 50 km

d) 46 km

Sol : Option B Explanation: Let the distance traveled = x. ∴ x / 9 – x / 10 = 32 / 60 → x = 48 km.

Q.5.Joseph walked 1 km/hr slower than usual and he could return home in 9/8th of his usual time. His normal walking rate is

a) 8 km/hr

b) 9 km/hr

c) 10 km/hr

d) 11 km/hr

Sol : Option B Explanation: Let his normal speed = x km/hr. Decreased speed = (x – 1) km/hr.
If usual time is t hrs, then on decreasing speed, he takes 9 / 8 of his usual time. But distance traveled on both sides is same. ∴ 9/8(x-1)t = tx → x = 9 km/hr.

Q.6.A man walks a km in b hours. The time taken to walk 200 m is

a) ab/200 hours

b) 200b/a hours

c) b/5a hours

d) a/5b hours

Sol : Option C Explanation: Speed of man = a/b km/hr. Distance to be traveled = 200 m = 0.2 km.
∴ Time taken = (0.2)/(a/b) → 0.2b / a→b/5a hours.

Q7.A car during its journey travels 30 minutes at a speed of 40 km/hr, another 45 minutes at a speed of 60 km/hr and 2 hours at a speed of 70 km/hr. Find its average speed (approximately).

a) 50 km/hr

b) 63 km/hr

c) 55.5 km/hr

d) 48 km/hr

Sol : Option B Explanation: Average speed = (Total distance)/(Total Time) →
=
= (20+45+140)/(13/4)
= 63 km/hr.

Q8.Find the time taken to cover the distance from Delhi to Agra, a distance of 360 km, by the Shatabdi express moving at 20 m/s.

a) 3 hours

b) 4 hours

c) 5 hours

d) 6 hours.

Sol : Option C Explanation: Moving at 20 m/s = 20 × (18/5) km/h= 72km/h. Time = 360 /72 = 5 hours.

Q9.Walking at 5/7^{th} of his usual speed, Kapil reaches the college 6 min late. Find Kapil’s usual time to reach college. A. B. C. D. B.

a) 15 min

b) 10 min

c) 5 min

d) 8 min

Sol : Option A Explanation: Let usual speed be x. Earlier time was d /x.
Now the time would be d / (5/7 x).
The difference between the two is 0.1 hour.
So the equation is (d / x) (7/5 – 1) = 0.1.
So usual time = d/x = 0.1× 5 / 2 = 0.25 hours = 15 minutes

Q10.Ram flew to Lanka in his Pushpak Vahan, at an average speed of 600 km/hr. On his way back along with Sita, because of the heavier baggage that he was carrying, his speed reduced to 400 km/hr. Find the average speed during the journey.

a) 520 km/hr

b) 440 km/hr

c) 480 km/hr

d) 560 km/hr

Sol : Option C Explanation: During the journey, Average Speed = 2 × 400 × 600 / (400 + 600)= 480 km /hr.