Question

A 3 cm wide border is printed on 100 sheets of paper , each of length 40 cm and breadth 30cm. If it costs(in rupees) Rs. 2.50 to print 100 sq cm of border, what is the total cost of printing the border ?

Answer 1

Here,

$AB=EF=HG=DC=40+3+3=46cm$

$EH=IL=JK=FG=30-3-3=24cm$

$AE=EI=JF=FB=KG=GC=LH=HD=3cm$

Area of printed border $=ar\left(ABFE\right)+ar\left(HGCD\right)+ar\left(EILH\right)+ar\left(JFGK\right)$

$=46\times 3+46\times 3+24\times 3+24\times 3+24\times 3$

$=138+138+72+72$

$=420c{m}^2$

$\Rightarrow$ Total area of printed border in $100$ sheets $=420\times 100$

$=42000c{m}^2$

$\Rightarrow$ $100c{m}^2$ of border cost $=Rs.2.5$

$\Rightarrow$ $1c{m}^2$ of border cost $=Rs.\frac{2.5}{100}$

$\Rightarrow$ Cost of printing $42000c{m}^2$ border $=Rs.\frac{2.5}{100}\times 42000$

$=Rs.1050$

$\therefore$ Total cost of printing border $=Rs.1050.$