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Q.

If the thickness of a pile of 12 cardboard sheets is 45 mm, then the thickness of a pile of 240 sheets is ____ cm.

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Detailed Solution

If the thickness of a pile of 12 cardboard sheets is 45 mm, then the thickness of a pile of 240 sheets is 90 cm.
Given the thickness of a pile of 12 cardboard sheets =45 mm.
We need to find the thickness of a pile of 240 sheets.
Using the fact that there are 10 mm in 1 cm, assume that the thickness of a pile of 240 sheets is

t

cm = 10

t

mm.
Understand that thickness of the pile is in direct proportion with number of sheets and hence the ratio of thickness and number of sheets is constant.

\Rightarrow \frac{thickness}{number of sheets} = constant

Equate the ratio of 45 mm and 12 sheet with 10

t

mm and 240 sheets to solve for

t

.

\frac{10 t}{240} = \frac{45}{12}

\Rightarrow \frac{t}{24} = \frac{15}{4}

\Rightarrow t = 24 \times \frac{15}{4}

\Rightarrow t = 6 \times 15

\Rightarrow t = 90

Hence, the thickness of a required pile of 240 sheets is 90 cm.

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