If 1/8th pencil is black, 1/4th pencil is white and remaining 5.25 cm is grey – what is total length of pencil? | Important MCQ with Explanation

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If 1/8th pencil is black, 1/4th pencil is white and remaining 5.25 cm is grey – what is total length of pencil?

7 cm
10.5 cm
8 cm
12 cm

Answer: 8 cm

Explanation

Black part = $1$ of the total length
White part = $1$ /4of the total length
Grey part = 5.25 cm
Total length =?

Let total length be $x$ cm.

Then:

$text{Black} = frac{1}{8}x, quad text{White} = frac{1}{4}x, quad text{Grey} = 5.25 , text{cm}$

Add them all:

$1/8 x + 1 x + 5.25 = x$

Convert $frac{1}{4}x$ to same denominator:

$frac{1}{8}x + frac{2}{8}x + 5.25 = x Rightarrow frac{3}{8}x + 5.25 = x$

Now solve:

$x - 3/8 x = 5.25 \Rightarrow 5/8 x = 5.25$

Multiply both sides by 8:

$5 x = 42 \Rightarrow x = 42 = 8.4 cm$

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