Question

Ram stuck four pictures each of length 10 cm and breadth 8cm on a chart paper of length 50 cm and breadth 40 cm. What area of the paper was left bare?
A. 1655 sq.cm
B. 1600 sq.cm
C. 1680 sq.cm
D. 1685 sq.cm

Answer 1

Hint: In the solution, it is given that the measurements of the chart and the picture, they are length and breadth, it means the chart is in rectangular shape, so we know that the area of the rectangle is the product of the length and the breadth. To find the remaining bare in the chart we have to subtract the total chart area and the area of the 4 pictures.

Complete step-by-step answer:

The number of pictures is \[n = 4\]
The length of each picture is \[l = 10\,{\rm{cm}}\].
The breadth of each picture is \[b = 8\,{\rm{cm}}\].
The length of the chart is \[L = 50\,{\rm{cm}}\].
The breadth of each picture is \[B = 40\,{\rm{cm}}\].
The equation of the area of the chart is
It can be see that the chart is in rectangle shape so the area of chart is
\[\Rightarrow A = L \times B\]
Substituting the values in the above equation, then
\[
\Rightarrow A = 50 \times 40\\
 = 2000\;{\rm{sq}}{\rm{.cm}}
\]
The equation of the area of the 1 pictures is
It can be see that the each picture is in rectangle shape so the area of 4 pictures is
\[\Rightarrow a = l \times b\]
Substituting the values in the above equation, then
\[
\Rightarrow a = 10 \times 8\\
 = 80\;{\rm{sq}}{\rm{.cm}}
\]
Then the area of four pictures is
\[
\Rightarrow a = 80 \times 4\\
 = 320\;{\rm{sq}}{\rm{.cm}}
\]
Now, the equation to find the remaining area to bare is
The remaining area =\[A - a\]
Substituting the values in the above equation, then
\[
\Rightarrow A - a = 2000\,{\rm{sq}}{\rm{.cm}} - 320\,{\rm{sq}}{\rm{.cm}}\\
 = 1680\;{\rm{sq}}{\rm{.cm}}
\]
So, the correct answer is “Option C”.

Note: We should be careful while finding the area of the pictures because there are four pictures, so firstly find the area of each picture and then product up with the 4 to get the 4 pictures area.