Question

A wooden beam cut into 2 pieces.
The length of the longer pieces is 58 of the total length of the beam.
The shorter wooden beam is 120 cm shorter than the longer piece.
Find the length of the wooden beam.

Answer 1

Correct Question:-

A wooden beam cut into 2 pieces.The length of the longer pieces is ⅝ of the total length of the beam. The shorter wooden beam is 120 cm shorter than the longer piece. Find the length of the wooden beam.

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Answer:-

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Given:

▪︎Length of longer peice = ⅝ of total beam

▪︎Length of shorter peice = Longer beam- 120cm

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To Find:

▪︎Total Length of wooden beam

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Solution:

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Let the total length of beam be x.

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As we know,

$\bf{}Total\ length\ of\ beam$$\bf{}= Longer\ peice + shorter\ peice$

$\sf{}\implies x = ⅝ of\ x + [(⅝ of\ x) - 120]$

$\sf{}\implies x = \frac{5x}{8}+ (\frac{5x}{8}-120)$

$\sf{}\implies x = \frac{5x+5x-960}{8}$

$\sf{}\implies x = \frac{10x-960}{8}$

$\sf{}\implies x ×8 = 10x - 960$

$\sf{}\implies 10x - 8x = 960$

$\sf{}\implies 2x = 960$

$\sf{}\implies x = 960 ÷ 2$

$\sf{}\therefore x = 480$

$\boxed{\bf{\pink{Hence, total\ length\ of\ beam\ is 480cm}}}$

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Verification:-

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Putting the value of x in equation;

$\sf{}\rightarrow 480 = ⅝ of\ 480 + [(⅝ of\ 480) - 120]$

$\sf{}\implies 480 = 300+(300-120)$

$\sf{}\implies 480 = 300 + 180$

$\sf{}\implies 480 = 480$

$\sf{}\therefore L.H.S. = R.H.S.$

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Hence, it is verified that answer is correct.

The length of wooden beam is 480cm.

Answer 2

Answer:

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