15 pastries and 12 biscuit packets have been donated for a school fete. These are to be packed in several smaller identical boxes with the same number of pastries and biscuit packets in each. How many biscuit packets and how many pastries will each box contain?

Given: 15 pastries and 12 biscuit packets have been donated for a school fete.

To find: Here we have to find the number of packets of pastries and biscuit if these are to be packed in several smaller identical boxes with the same number of pastries and biscuit packets in each.

Solution:

Pastries and biscuit packets are to be packed in several smaller identical boxes with the same number of pastries and biscuit packets in each.

The required number of boxes which will contain an equal number of both pastries and biscuits will be the HCF of 15 and 12.

Using Euclid's division algorithm to find HCF:

Using Euclid’s lemma to get: 

• $15\ =\ 12\ \times\ 1\ +\ 3$

Now, consider the divisor 12 and the remainder 3, and apply the division lemma to get:

• $12\ =\ 3\ \times\ 4\ +\ 0$

The remainder has become zero, and we cannot proceed any further. 

Therefore the HCF of 15 and 12 is the divisor at this stage, i.e., 3.

So, the total number of boxes are 3.

Therefore,

Number of pastries each box contain  $=\ \frac{15}{3}\ =$  5

Number of biscuit packets each box contain  $=\ \frac{12}{3}\ =$  4

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Updated on: 10-Oct-2022

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