Exercise : 2


1. With a uniform speed a car covers a distance in 8 hours. Were the speed increased by 4 km/hr the same distance could be covered in 712 hours. What is the distance covered?
(a) 640 km
(b) 480 km
(c) 420 km
(d) Cannot be determined
(e) None of these
Ans.b

Here D7.5 - D8 = 4

(where D is the distance in km)

⇒ 0.5 D = 4 × 8 × 7.5

⇒ D = 2 × 4 × 8 × 7.5 = 480 km

2. A 300-metre-long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
(a) 320 metres
(b) 650 metres
(c) 350 metres
(d) Data inadequate
(e) None of these
Ans.c

When a train crosses a platform, it crosses a distance equal to the sum of the length of the platform and that of the train. But when a train crosses a signal pole, it crosses the distance equal to its length only.

Here, time taken by the train to cross a signal pole = 18 seconds

Hence, speed of the train = 30018 m/sec

The train takes 21 = (39 – 18) seconds extra in order to cross the platform.

Hence, length of platform = \(\frac{21 \times 300}{18} = 350 m\)

3. A 260-metre-long train crosses a 120-metre-long wall in 19 seconds. What is the speed of the train?
(a) 27 km/hr
(b) 49 km/hr
(c) 72 km/hr
(d) 70 km/hr
(e) None of these
Ans.c

Speed of train = \(\frac{260 + 120}{19} \times \frac{18}{5} = 72 \; km/hr\)

4. A 270-metre-long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 secs. What is the length of the other train?
(a) 240 metres
(b) 320 metres
(c) 260 metres
(d) 230 metres
(e) None of these
Ans.d

Relative speed = 120 + 80 kmph = 200 × 518 m/sec

t = \(\frac{Distance}{Speed} = \frac{\left(270 + x \right) \times 9}{500}\)

or 270 + x = \(\frac{9 \times 500}{9}x\) = 500 – 270 = 230 m

5. A monkey ascends a greased pole 12 metres high. He ascends 2 metres in first minute and slips down 1 metre in the alternate minute. In which minute, he reaches the top ?
(a) 21st
(b) 22nd
(c) 23rd
(d) 24th
(e) None of these
Ans.b

In 2 minutes, he ascends = 1 metre

∴ 10 metres, he ascends in 20 minutes.

∴ He reaches the top in 21st minute.

6. A man walks a certain distance and rides back in 614h. He can walk both ways in 734h. How long it would take to ride both ways ?
(a) 5 hours
(b) 412 hours
(c) 434 hours
(d) 6 hours
(e) None of these
Ans.c

We know that, the relation in time taken with two different modes of transport is

twalk both + tride both = 2 (twalk + tride)

314 + tride both = 2 × 254

⇒ tride both = 252 - 314 = 194 = 434 hours

7. There are 20 poles with a constant distance between each pole. A car takes 24 seconds to reach the 12th pole . How much time will it take to reach the last pole?
(a) 25.25 s
(b) 17.45 s
(c) 35.75 s
(d) 41.45 s
(e) None of these
Ans.d

Let the distance between each pole be x m.

Then, the distance up to 12th pole = 11 xm

Speed = 11x24 m/s

Time taken to covers the total distance of 19x

= \(\frac{19x \times 24}{11x} = 41.45 \; s\)

8. A man is walking at a speed of 10 km per hour. After every kilometre, he takes rest for 5 minutes. How much time will be take to cover a distance of 5 kilometres?
(a) 48 min.
(b) 50 min.
(c) 45 min.
(d) 55 min.
(e) None of these
Ans.b

Rest time = Number of rest × Time for each rest

= 4 × 5 = 20 minutes

Total time to cover 5km

= (510 × 60)minutes + 20 minutes = 50 minutes

9. On a journey across Bombay, a tourist bus averages 10 km/h for 20% of the distance, 30 km/h for 60% of it and 20 km/h for the remainder. The average speed for the whole journey was
(a) 10 km/h
(b) 30 km/h
(c) 5 km/h
(d) 20 km/h
(e) None of these
Ans.d

Let the average speed be x km/h.

and Total distance = y km. Then,

0.210y + 0.630y + 0.220y = yx

⇒ x = 10.05 = 20 km/h

10. In a 800 m race around a stadium having the circumference of 200 m, the top runner meets the last runner on the 5th minute of the race. If the top runner runs at twice the speed of the last runner, what is the time taken by the top runner to finish the race ?
(a) 20 min
(b) 15 min
(c) 10 min
(d) 5 min
(e) None of these
Ans.c

After 5 minutes (before meeting), the top runner covers 2 rounds i.e., 400 m and the last runner covers 1 round
i.e., 200 m.

∴ Top runner covers 800 m race in 10 minutes.