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Standard VIII

Mathematics

Applications (Word Problem)

A piece of st...

Question

A piece of string is $80$ cm long. It is cut into three pieces. The longest piece is $3$ times as long as the middle sized piece and the shortest piece is $46$ cm shorter than the longest piece. Find the length of the shortest piece.

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Solution

The correct option is B $8$ cm
Let the length of middle piece $=$ $x$
Then length of longest piece $=$ $3 x$
Then length of shortest piece $=$ $3 x - 46$
Thus, $x + 3 x + 3 x - 46 = 80$
$\Rightarrow 7 x = 126$
$\Rightarrow x = 18$
Hence, shortest piece $=$ $18 \times 3 - 46 = 54 - 46 = 8$ cm

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A piece of string is 80 cm long. It is cut into three pieces. The longest piece is 3 times as long as the middle sized piece and the shortest piece is 46 cm shorter than the longest piece. Find the length of the shortest piece.

The correct option is B 8 cmLet the length of middle piece = xThen length of longest piece = 3xThen length of shortest piece = 3x−46Thus, x+3x+3x−46=80⇒7x=126⇒x=18Hence, shortest piece = 18×3−46=54−46=8 cm

A piece of string is $80$ cm long. It is cut into three pieces. The longest piece is $3$ times as long as the middle sized piece and the shortest piece is $46$ cm shorter than the longest piece. Find the length of the shortest piece.

The correct option is B $8$ cm
Let the length of middle piece $=$ $x$
Then length of longest piece $=$ $3 x$
Then length of shortest piece $=$ $3 x - 46$
Thus, $x + 3 x + 3 x - 46 = 80$
$\Rightarrow 7 x = 126$
$\Rightarrow x = 18$
Hence, shortest piece $=$ $18 \times 3 - 46 = 54 - 46 = 8$ cm