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Q.

In an exhibition hall, there are 24 display boards each of length 1m 50 cm and breadth 1m. There is a 100m long aluminum strip, which is used to frame these boards. Then, the length is ____ m of the cloth used, if its breadth is 120 cm.

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Detailed Solution

In an exhibition hall, there are 24 display boards each of length 1m 50 cm and breadth 1m. There is a 100m long aluminum strip, which is used to frame these boards. Then, the length is 30 m of the cloth used, if its breadth is 120 cm.
Given that,
Length of one display board = 1m + 50 cm
= 1 m

+

\frac{50}{100}

m
= 1 + 0.5
= 1.5 m
Breadth of the display board = 1m.
We have to find the length of the cloth used, if its breadth is 120cm.
First, we will find the area required for 24 display boards.
Area required for 24 display boards = 24

\times

(l

\times

b)
= 24

\times

(1.5

\times

1)
= 24

\times

1.5
= 36
Therefore, the area required for 24 display boards is 36 sq. m.
Now, to find length of the cloth used,
Breadth = 120 cm
=

\frac{120}{100}

= 1.2 m
Area of display board = Length of the cloth

\times

Breadth of the cloth
∴ Length of the cloth =

\frac{Area of display board}{Breadth of the cloth}

=

\frac{36}{1.2}

= 30 m.
Hence, the length of the cloth used, if its breadth is 120cm is 30 m.

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