Question

Mark the correct alternative in the following question:

How many envelopes can be made out of a sheet of paper 72 cm by 48 cm, if each envelope requires a paper of size 18 cm by 12 cm?

(a) 4 (b) 8 (c) 12 (d) 16

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \mathrm{length}\mathrm{of}\mathrm{the}\mathrm{sheet}\mathrm{of}\mathrm{the}\mathrm{paper}=72\mathrm{cm}, \\ \mathrm{breadth}\mathrm{of}\mathrm{the}\mathrm{sheet}\mathrm{of}\mathrm{the}\mathrm{paper}=48\mathrm{cm}, \\ \mathrm{length}\mathrm{of}\mathrm{the}\mathrm{envelope}=18\mathrm{cm}\mathrm{and} \\ \mathrm{breadth}\mathrm{of}\mathrm{the}\mathrm{envelope}=12\mathrm{cm} \\ \mathrm{The}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{sheet}\mathrm{of}\mathrm{the}\mathrm{paper}=\mathrm{length}\times \mathrm{breadth} \\ =\left(72\times 48\right){\mathrm{cm}}^2 \\ \mathrm{And},\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{envelope}=\mathrm{length}\times \mathrm{breadth} \\ =\left(18\times 12\right){\mathrm{cm}}^2 \\ \mathrm{Now},\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{envelope}\mathrm{that}\mathrm{can}\mathrm{be}\mathrm{made}\mathrm{out}=\frac{\mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{sheet}\mathrm{of}\mathrm{the}\mathrm{paper}}{\mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{envelope}} \\ =\frac{\left(72\times 48\right)}{\left(18\times 12\right)} \\ =4\times 4 \\ =16 \end{gathered}$$

Hence, the correct alternative is option (d).