Unitary method is a method in which you find the value of a unit and then the value of a required number of units. What can units and values are?

Suppose you go to the market to purchase 6 apples. The shopkeeper tells you that he is selling 10 apples for Rs 100. In this case, the apples are the units and the cost of the apples is the value. While solving a problem using unitary method, it is important that you recognize the units and values.

For simplification, always write the things to be found on the right hand side and things known on the left hand side. In the above problem, we know the amount of number of apples and the value of the apples is unknown.

Consider another example, a car runs 150 km on 15 litre of fuel, how much kilometer will it run on 10 litre of fuel?

In the above example, try and identify units (known) and values (unknown).

Kilometer = Unknown (Right Hand Side)

No of litres of fuel = Known (Left Hand Side)

Now we will try and solve this problem.

15 litres = 150 km

1 litre = 150/15 = 10 km

10 litres = 10 x 10 = 100 km

The car will run 100 kilometers on 10 litres of fuel.

Unitary method finds its practical application everywhere ranging from problems of speed, distance, time to problems related to calculating the cost of materials.

Let us take another problem on the unitary method.

**Illustration**: **A car traveling at a speed of 140 kmph covers 420 km. How much time will it take to cover 280 km?**

**Solution**: First we need to find the time required to cover 420 km.

Speed = Distance/Time

140 = 420/T

T = 3 hours

Applying unitary method,

420 km = 3 hours

1 km = 3/420 hour

280 km = (3/420) x 280 = 2 hours

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