\(\frac{1}{8}\)th part of a pencil is black and \(\frac{1}{2}\) part of the remaining is white. If the remaining part is blue and length of this blue part is 3\(\frac{1}{2}\) cm, then find the length of the pencil.

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Bihar Police Constable Memory Based Paper (Held On: 01 Oct, 2023 Shift 2)

Answer 1

Given:

Part of Black Pencil = \(\dfrac{1 }{8} \)

Part of white Pencil = \(\dfrac{1 }{2} \)

the remaining \(3\dfrac{1}{2}\)is blue

Calculation:

Let the total length of the pencil be LCM of \(\dfrac{1 }{8} \) and \(\dfrac{1 }{2} \) = 16x

Length of black colour =\(\dfrac{1 }{8} \)× 16x = 2x

Remaining = 16x - 2x = 14x

Length of white colour = \(\dfrac{1}{2} \) × 14x = 7x

The remaining \(3\dfrac{1}{2}\) is blue.

Remaining = 14x - 7x = 7x = \(\dfrac{7 }{2} \)

⇒ x = \(\dfrac{1 }{2} \)

Total length of the pencil = 16x = 16 × \(\dfrac{1 }{2} \) = 8m

∴ Option 3 is the correct answer.

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