Dear Reader,
Below are three sample speed - time questions for your practice.

Question 1

Two goats were standing 700 metres apart. One goat is standing at the western gate and another is standing at eastern gate. They move forward for two minutes at the rate of 50 metres per minute initially. Then they move backward for two minutes at the rate of 25 metres per minute. The process continues. When will the two goats meet/hit the other?

a) 20 min b) 22 min c) 26 min d) 28 sec

Answer : b) 22 min.

Solution :

For every 2 min. the two goats will come nearer by 200 metres. In the next 2 min. the two goats will go backwards 50 metres back and hence after every 4 minutes goats would have come nearer by 100 metres. The process continues. Hence after 20 min the two goats would have come nearer by 500 metres. At the end of 22 mins the two goats will meet each other.

Question 2

A new type of study about movement of trains was conducted by South Central Railway. Two trains are standing 2520 metres apart in two adjacent railway lines. Both the trains move for five seconds at 60 m/sec. They halt for 12 seconds. Then again they start moving for five second at 60 m/sec. The process continues. After how many seconds will the engines of the two trains cross in the adjacent railway lines?

a) 50 sec b) 60 sec c) 70 sec d) none of these.

Answer : c) 70 sec.

Solution :

The two trains are standing 2520 metres apart in two adjacent railway lines. After every five second they come closer by 600 metres.(300 + 300). They halt for 12 seconds and then start moving. So after every 17 seconds they come closer by 600 metres. The process continues. After 68 second they would have covered 2400 metres. So in the next two seconds that is after 70 second the engines of the two trains will cross each other in adjacent line having covered 2520 metres.

Question 3

Kumaresan Environment Industries Limited , planted a tree. The tree was growing at 6 cm every day. The tree was allowed to grow for ten days. On the 11th day the tree will be cut to 50% of its size. From the next day (12th day) for the next ten days it was allowed to grow at the rate of 6 cm every day. On the 11th day the tree is cut to 50% of its size. The process continued. Assuming the tree was planted afresh as a seed after how many days the tree would have reach a height of 105 cms?

a) 32 days b) 26 days c) 18 days d) none of these.

Answer : a) 32 days

Solution :

For ten days the tree grows at 6 cm per day and it will reach a height of 60 cm.
On the 11th day its height will be reduced to 50% of its size – 30 cm.
Till 21st day the tree will grow further 60 cm and reach a height of 90 cms.
On 22nd day its height would have been reduced to 45 cm.(50%)
It grows at 6 cm per day and on 32nd day it would have grown further 60 cm and reached height of 105 cms.