Question

The thickness of 400 sheets of paper is \[4.5cm\]
1) What would be the thickness of 24 quires of sheets? [1 quire \[ = 25\] sheets of paper]
2) How many sheets of paper would be there in a pile which is \[13.5cm\] thick?

Answer 1

Hint:
Here we need to find the thickness of the given number of sheets. We will first convert the queries into the number of sheets of paper. Then we will find the thickness of one sheet and then we will use the unitary method to find the required thickness of the given number of sheets.

Complete step by step solution:
1) Here we need to find the thickness of 24 quires of sheets.
We know that 1 quire is equal to 25 sheets of paper.
Therefore,
 \[24{\rm{ quires}} = 24 \times 25 = 600{\rm{ sheets of paper}}\]
It is given that the thickness of 400 sheets of paper is equal to \[4.5cm\].
Now, we will use the unitary method to find the thickness of 600 sheets.
Thickness of 400 sheets of paper is equal to \[4.5cm\]
Using the unitary method here, we get
 Thickness of 1 sheet of paper is equal to \[\dfrac{{4.5}}{{400}}cm\]
Again using the unitary method here, we get
Thickness of 600 sheet of paper is equal to \[\dfrac{{4.5}}{{400}} \times 600cm = 6.75cm\]
Hence, the thickness of 24 quires of sheets is equal to \[6.75cm\].

2) Here, we need to find the number of sheets of paper that would be there in a pile which is \[13.5cm\] thick
Here also we will use the unitary method.
\[4.5cm\] thick pile contains 400 sheets
Using the unitary method here, we get
\[1cm\] thick pile contains \[\dfrac{{400}}{{4.5}}\] sheets
Again using the unitary method here, we get
\[13.5cm\] thick pile contains \[\dfrac{{400}}{{4.5}} \times 13.5 = 1200\] sheets

Hence, 1200 sheets of paper would be there in a pile which is \[13.5cm\] thick.

Note:
Here we used the unitary method to obtain the thickness and number of sheets. So we need to know more about it to use it in different types of problems. The unitary method is defined as a method in which we find the value of a unit and then we find the value of a required number of units.
To find the number of sheets of thickness of \[13.5cm\] pile we have to first find the thickness 1 cm pile. Using the thickness of 1 cm thick pile we can find any number of sheets of the given thickness.