The first arithmetic topic that will be dealt with here is Time and Distance along with Unitary method.
Later principles of BODMAS will be taken up.
Another important topic that will be looked into is Time and Work.

Tuesday, February 5, 2013

Unitary Method with Time and Distance - 1

The problem: A bus covers a distance of 660 kilometres (km) in 5 hours 30 minutes. Find the speed of the bus per hour.

Solution: 1 hour = 60 minutes
Therefore, 5 hours 30 minutes = 5 x 60 minutes + 30 minutes = 330 minutes
We have to find out how far the bus can travel in 60 minutes.
Now, the bus takes 330 minutes to travel 660 km. (the prime statement)

So the bus takes '1 minute' to travel 660/330 km

Therefore the bus takes '60 minutes' to travel 660/330 x 60 km = 120 km.

Answer: The speed of the bus per hour is 120 km.

In this problem we have used Unitary Method. It is a very, very important tool in arithmetic. In this method we construct the first statement, referred to in the solution as the prime statement, in a way so that the quantity or parameter that we have to find out is kept at the end of the statement.  The other parameter (or parameters) is kept at the front of the prime statement.

This construction of the prime (beginning) statement is very important. It guides us throughout the whole solution until we arrive at the answer. Here it is the speed of the bus expressed in km. So we have kept km at the end of our prime statement, and time at the front. 

In the next statement, we have to convert the first parameter, in this problem the time, into unity or 1. Hence the name Unitary Method. If time becomes 1 minute, then the distance covered by the bus will also get reduced. Hence we have divided 660 by 330. Here is the logical play of our brain. (There may be problems where, instead of division, we may have to perform multiplication.) 

In the next statement we simply replace the unity by the desired value, here "1 minute" by 60 minutes" to get the desired distance in km, and accordingly we have multiplied (as 60 minutes' distance will be greater than 1 minutes' distance) 660/330 by 60. 

Here we are dealing with just two parameters, namely time taken and distance covered. There may be more than two parameters, which will be discussed in a later post. The rule of Unitary Method remains all the same there also.

Try out the following problem yourself:

A train covers a distance of 500 km in 2 hours 5 minutes. Find the speed of the train per hour.  
Answer: Speed of the train is 240 km per hour. 

Please feel free to ask any question through the comment box.

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