An order was placed for supply of carpet of breadth 3 metres, the length of carpet was 1.44 times of breadth. Subsequently the breadth and length were increased by 25 and 40 percent respectively. At the rate of 45 per square metre, what would be the increase in the cost of the carpet ?

Solution(By Examveda Team)

Original breadth = 3 m
Original length :
$$\eqalign{ & = \left( {1.44 \times 3} \right)m \cr & = 4.32\,m \cr} $$
New breadth :
$$\eqalign{ & = \left( {125\% {\text{ of 3}}} \right)m \cr & = \left( {\frac{{125}}{{100}} \times 3} \right)m \cr & = 3.75\,m \cr} $$
New length :
$$\eqalign{ & = \left( {140\% {\text{ of 4}}{\text{.32}}} \right)m \cr & = \left( {\frac{{140}}{{100}} \times 4.32} \right)m \cr & = 6.048\,m \cr} $$
Original area :
$$\eqalign{ & = \left( {4.32 \times 3} \right){m^2} \cr & = 12.96\,{m^2} \cr} $$
New area :
$$\eqalign{ & = \left( {6.048 \times 3.75} \right){m^2} \cr & = 22.68\,{m^2} \cr} $$
Increase in area :
$$\eqalign{ & = \left( {22.68 - 12.96} \right){m^2} \cr & = 9.72\,{m^2} \cr} $$
∴ Increase in cost :
$$\eqalign{ & = {\text{Rs}}{\text{. }}\left( {9.72 \times 45} \right) \cr & = {\text{Rs}}{\text{.}}\,{\text{437}}{\text{.40}} \cr} $$