March 27, 2023

# Unitary method

The unitary approach is a methodology for problem-solving that involves first determining the value of a single unit, and then determining the necessary value by multiplying the single unit value. In essence, this technique is used to determine the value of a unit from the value of a multiple. The unitary method is also known as the method of ones. The main principle of this approach is that we multiply to obtain more value. By dividing, we obtain less value. For example:

Example 1: The cost of one almirah  is Rs. 3575 . Find the cost of 8 almirahs.

Solution: Clearly more almirahs will cost more and , more we get on multiplying.

Cost of 1 almirah =  Rs. 3575

Cost of 8 almirahs = Rs. (3575 x 8)

=Rs. 28600 .

Hence, the cost of 8 almirahs is Rs. 28600 .

Example 2 : The cost of 17 books is rs. 1445. Find the cost of one book.

Solution : Clearly, less books will cost less and less we get on dividing.

Cost of 17 books =  Rs. 1445

$\therefore$

Cost of 1 book =  Rs. ($1445\div&space;17)$

=  Rs. 85

Hence , the cost of 1 book is Rs. 85.

Example 3: 14 apples cost ₹204. What is the cost of 73 such apples?

We have, The cost of 14 apples

$\begin{array}{r}= Rs.\left[extract_itex\right]204\left[/extract_itex\right]\end{array}$

∴ The cost of 1 apple =$204\div&space;14=Rs.14.57$

The cost of 73 apples = 14.57 x 73 = Rs. 1063.71

From the above example , we conclude the following

(i) If the price of one such item is known, we can calculate the price of any other number of identical goods by multiplying the price by the number of items.

(ii) If the total price of several identically priced goods is known, we may calculate the price of one item by dividing the total price by the specified quantity of items.

(iii) When the price of a set number of the same kind of objects is known, and we need to figure out the price of an additional set of those items, we first compute the price of one item, and then multiply the result by the necessary number of items.

## Unitary method for class 5 ( solved questions )

Example 1: Buttons are packed in packets of 576 each . How many buttons are there in 48 such packets?

Solution: More packets will contain more buttons.

Number of buttons in 1 packet = 576

Number of buttons in 48 packets = 576 x 48

=27648 .

Hence , there are 27648 buttons in 48 packets.

Example 2:  The annual rent of a house is Rs. 58500. What is its rent for 17 months?

Solution:   Since , 1 year = 12 months

Rent for 12 months =  Rs.58500

Rent for 1 month = Rs. $58500\div&space;12=&space;Rs.4875$

So rent for 17 months =  Rs. 4875 x  17 =  Rs. 82875

Hence the rent for 17 months is Rs. 82875

Example 3: A shopkeeper sold 136 almirahs for Rs. 3784 each. From the money so received, he bought 34 refrigerators. What is the cost of each refrigerator?

Solution: More almirah will cost more.

Cost of 1 almirah = Rs. 3784 .

Cost of 136 almirahs = Rs. 3784 x 136

= Rs. 514624

Now, less refrigerator will cost less.

Cost  of 34 refrigerators = Rs. 514624

Cost of 1 refrigerator = Rs. 514624 $\div$ 34

= Rs. 15136

Hence, the cost of each refrigerator  is Rs. 15136

Example 4: A factory  produces 6816 motor horns in 12 days . How many horns does it produce in three weeks ?

Solution :  Number of horns produce in 12 days = 6816

Number of horns produce in 1 days = 6816 $\div&space;12$

=  568

Number of horns produce in 3 weeks (= 21 days) =  568 x 21

=11928

Hence the company will produce 11928 horns in 3 weeks.

Example 5: Three planes can carry 1185 passengers. How many passengers can be carried in 8 planes?

Solution :  Number of passengers in 3 planes = 1185

Number of passengers in 1 planes = 1185 $\div$ 3

=395

Number of passengers in 8 planes = 395 x 8

= 3160

Hence , 8 planes can carry 3160 passengers.