Question

A table cover \[6m\times 3m\] is spread on a meeting table. If \[25cm\] of the table cover is hanging all around the table, find the cost of polishing the top of the table at \[\text{Rs}.12\] per square meter.

Answer 1

Hint: To find the total cost of polishing the table top we need to find the area without the cloth hanging and after that we need to multiply that area with the cost of polishing per square meter. The formula required to find the total cost is
Area of the table needed to polish \[\text{Are}{{\text{a}}_{\text{Polish}}}\] is given as:
\[\text{Are}{{\text{a}}_{\text{Polish}}}=\left[ \text{Lengt}{{\text{h}}_{\text{Table}}}\text{-}\left( \text{Lengt}{{\text{h}}_{\text{Hanging}}} \right)\text{ }\!\!\times\!\!\text{ Lengt}{{\text{h}}_{\text{Table}}} \right]\text{ }\!\!\times\!\!\text{ }\left[ \text{Breadt}{{\text{h}}_{\text{Table}}}\text{-}\left( \text{Lengt}{{\text{h}}_{\text{Hanging}}} \right)\text{ }\!\!\times\!\!\text{ Breadt}{{\text{h}}_{\text{Table}}} \right]\]
And the cost of the polishing is \[\text{Are}{{\text{a}}_{\text{Polish}}}\times \text{Pric}{{\text{e}}_{\text{per meter}}}\]
where \[Lengt{{h}_{Table}}\] is the length of the table in meters and \[Breadt{{h}_{Table}}\] is the breadth of the table in meters and \[Lengt{{h}_{Hanging}}\] is the length of the table cover hanging all around the table, \[\text{Pric}{{\text{e}}_{\text{per meter}}}\] is the cost of polishing per meter.

Complete step-by-step answer:
Let us place the dimensions in the formula we get the value of the total area we need to polish is:
\[\text{Are}{{\text{a}}_{\text{Polish}}}=\left[ \text{Lengt}{{\text{h}}_{\text{Table}}}\text{-}\left( \text{Lengt}{{\text{h}}_{\text{Hanging}}} \right)\text{ }\!\!\times\!\!\text{ Lengt}{{\text{h}}_{\text{Table}}} \right]\text{ }\!\!\times\!\!\text{ }\left[ \text{Breadt}{{\text{h}}_{\text{Table}}}\text{-}\left( \text{Lengt}{{\text{h}}_{\text{Hanging}}} \right)\text{ }\!\!\times\!\!\text{ Breadt}{{\text{h}}_{\text{Table}}} \right]\]
Convert the dimensions into meters.
\[\text{Are}{{\text{a}}_{\text{Polish}}}=\left[ \text{6-}\left( \text{0}\text{.25} \right)\text{ }\!\!\times\!\!\text{ 6} \right]\text{ }\!\!\times\!\!\text{ }\left[ \text{3-}\left( \text{0}\text{.25} \right)\text{ }\!\!\times\!\!\text{ 3} \right]\]
\[\text{Are}{{\text{a}}_{\text{Polish}}}=\left[ \text{4}\text{.5} \right]\text{ }\!\!\times\!\!\text{ }\left[ \text{2}\text{.25} \right]\]
\[\text{Are}{{\text{a}}_{\text{Polish}}}=\text{10}\text{.125 }{{\text{m}}^{2}}\]
Hence, the area of the table to be polished is \[\text{10}\text{.125 }{{\text{m}}^{2}}\].
The total price of polishing the table at the price of \[\text{Rs}.12\] per square meter is
\[\text{10}\text{.125 }{{\text{m}}^{2}}\times \text{Rs}.12=\text{Rs}.121.5\]

\[\therefore \] The total costing price of polishing the table is \[\text{Rs}.121.5\].

Note: Students may go wrong while working with the extra cloth that is hanging, the extra cloth dimension needs to be subtracted from both length and breadth. The part is not external but internal part of length and breadth as \[25\text{ }cm\] part of both length and breadth are hanging and needed to be left out, the length and breadth we need are \[\text{Lengt}{{\text{h}}_{\text{Table}}}\text{-}\left( \text{Lengt}{{\text{h}}_{\text{Hanging}}} \right)\text{ }\!\!\times\!\!\text{ Lengt}{{\text{h}}_{\text{Table}}}\] and \[\text{Breadt}{{\text{h}}_{\text{Table}}}\text{-}\left( \text{Lengt}{{\text{h}}_{\text{Hanging}}} \right)\text{ }\!\!\times\!\!\text{ Breadt}{{\text{h}}_{\text{Table}}}\].