Unitary Method
Consider the following situations:
Example 1
Two friends Reshma and Seema went to market to purchase notebooks. Reshma purchased 2 notebooks for 24 rupees . What is the price of one notebook?
Solution :
Cost of 2 notebooks is
Therefore, cost of 1 notebook =
Now, if you were asked to find cost of 5 such notebooks. It would be = Rs. 12 ×
Example 2
A scooter requires 2 litres of petrol to cover 80 km. How many litres of petrol is required to cover 1 km? These are examples of the kind of situations that we face in our daily life. How would you solve these?
Solution :
Reconsider the second example: We want to know how many litres are needed to travel 1 km.
For 80 km, petrol needed =
Therefore to travel 1 km, petrol needed =
Now, if you are asked to find how many litres of petrol are required to cover 120 km?
Then petrol needed =
The method in which first we find the value of one unit and then the value of required number of units is known as Unitary Method.
Let's try out a few more problems.
Try these
| Time | Distance travelled by Karan | Distance travelled by Kriti |
|---|---|---|
| 2 hours | 8 km | 6km |
| 1 hour | 4km | |
| 4 hours |
We see that,
Distance travelled by Karan in 2 hours = 8 km
Distance travelled by Karan in 1 hour =
Therefore, distance travelled by Karan in 4 hours = 4 × 4 =
Similarly, to find the distance travelled by Kriti in 4 hours, first find the distance travelled by her in 1 hour.
If the cost of 6 cans of juice is ₹ 210 , then what will be the cost of 4 cans of juice?
Solution :
Cost of 6 cans of juice = ₹ 210
Therefore, cost of one can of juice =
Therefore, cost of 4 cans of juice = 35 × 4 = ₹
Thus, cost of 4 cans of juice is ₹ 140.
A motorbike travels 220 km in 5 litres of petrol. How much distance will it cover in 1.5 litres of petrol?
Solution :
In 5 litres of petrol, motorbike can travel 220 km
Therefore in 1 litre of petrol, motor bike travels =
Therefore in 1.5 litres, motorbike travels =
Thus, the motorbike can travel 66 km in 1.5 litres of petrol.
If the cost of a dozen soaps is Rs. 153.60, what will be the cost of 15 such soaps?
Solution :
We know that 1 dozen =
Thus, cost of 12 soaps = Rs.153.60
Therefore, cost of 1 soap =
Total cost of 15 soaps = Rs. 12.80 × 15 = Rs.
Thus, cost of 15 soaps is Rs. 192.
Cost of 105 envelopes is Rs 350. How many envelopes can be purchased for Rs 100?
Solution :
In Rs. 350, the number of envelopes that can be purchased =
Therefore in Rs. 1, number of envelopes that can be purchased =
In Rs. 100, the number of envelopes that can be purchased =
Thus, 30 envelopes can be purchased for Rs. 100.
A car travels 90 km in
Solution :
Thus, 90 km is covered in 150 minutes.
Therefore, 1 km can be covered in
Therefore, 30 km can be covered =
Thus, 30 km can be covered in 50 minutes.