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**Time,Distance and Work Shortcuts**

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**Question 1:** A
train running at 25 km/hr takes 18 seconds to pass a platform. Next, it
takes 12 seconds to pass a man walking at 5 km/hr in the opposite
direction. Find the sum of the length of the train and that of the
platform.

(1) 125 m(2) 135 m

(3) 145 m

(4) 155 m

**Solution:**

Speed of train = 25 km./hr.

Distance travelled in 18 secs at this speed

Where D = L .

_{train}+ L .

_{platform}

length of train + length of platform = 125 m.

**Short Trick:**

Speed in m/sec.

Sum of length of train & Platform

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**Question 2:** Two
trains for Delhi leave Jaipur at 8.30 a.m. and 9.00 a.m. and travel at
60 km/hr and 75 km/hr respectively. How many km. away from Delhi will
the two trains meet.

(1) 125 km(2) 150 km

(3) 175 km

(4) 200 km

**Solution:**

Distance covered by 1

^{st}train in 30 min. = 30 kms. (as speed per hrs. 60)

Time taken by 2

^{nd}train to cover 30 kms. = 2 hrs. (as it travels 15 km. per hr. more than 1

^{st}train. Hence takes 2 hrs. to cover 30 km. that 1

^{st}train has already covered)

Dist. covered = (60 x 2.5 hr.) or (75 x 2 hrs.) =

**150 km.**

**Short Trick:**

Required distance = (9.00 – 8.30) x

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**Question 3: **Two
places P and Q are 162 km apart. A train leaves P for Q and at the same
time another train leaves Q for P. Both the trains meet 6 hrs after
they start moving. If the train travelling from P to Q travels 8 km/hr
faster than the other train, find the speed of the two trains.

(1) 17.5 km/hr, 9.5 km/hr(2) 19.5 km/hr, 11.5 km/hr

(3) 21.5 km/hr, 13.5 km/hr

(4) Can't be determined

**Solution:**

Suppose the speeds of the two trains are p km/hr and q km/hr respectively. Thus

and p – q = 8 …… (ii)

(i) + (ii) implies that

2p = 35 p = 17.5 km/hr

and (i) – (ii) implies that

2q = 19 q = 9.5 km/hr

**Short Trick:**

Take speed =

(x) + (x + 8) = 27 (as given diff. in speed = 8 kms./hr.)

9.5 & 17.5

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**Question 4: **A train running at a speed of 60 kmph crosses a platform double its length in 32.4 seconds. What is the length of the platform?

(1) 180 metres(2) 240 metres

(3) 360 metres

(4) 90 metres

**Solution:**

Let the length of the train be x m

length of the platform = 2x m

Total distance covered by the train = (2x + x =) 3x m

Now, according to the question

or,

**Short Trick:**

Speed in m/sec

Distance covered

Total length

540

(as the length of platform is double of the train)

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**Question 5:** A
train travels at the speed of 65 kms/hr and halts at 8 junctions for a
certain time. It covers a distance of 1300 kms in 1 day (24 hours). How
long does the train stop at each junction, if it halts for the same
period of time at all the junctions?

(1) 30 minutes(2) 20 minutes

(3) 60 minutes

(4) 40 minutes

**Solution:**

Speed = 65 kmph

Distance = 1300 kms

Time taken

Clearly, 4 hours are spent at 8 junctions in stoppages as one full day was taken for the journey to be completed.

Required time = 4 x 60 = 240 min. and at each junction the halt is of

**Short Trick:**

Time to cover 1300 km=D/S = 1300/65= 20 hrs

Break = 24 hrs. – 20 hrs. = 4 hrs.

Break at each junction = 30 min

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