Question

Yogesh require 3 days more than Vivek to do work. If both of them work

together, the work can be completed in 2 days. Find number of days require

by each of them to complete the work​

Answer 1

Step-by-step explanation:

Yogesh require 3 days more than Vivek to do work. If both of them work

together, the work can be completed in 2 days. Find number of days require

by each of them to complete the work

Answer 2

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

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• Yogesh require 3 days more than Vivek to do work
• Both can complete the work in 2 days

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$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

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• No. of days required by both to complete the work .

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$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

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let vivek complete the work in x days

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Therefore Yogesh will complete the work in x + 3 days .

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$\sf{\red{\boxed{\bold{1\: day\: work = \dfrac{1}{Total\: time\: taken}}}}}$

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1 day's work of vivek = 1 / x

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1 day's work of Yogesh = 1 / x + 3

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(Vivek + yogesh)'s 1 day work = 1 / 2

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Acc. to the question :-

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$\sf : \implies\: {\bold{ \dfrac{1}{x} + \dfrac{1}{x+3}= \dfrac{1}{2}}}$

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$\sf : \implies\: {\bold{ \dfrac{x+3 +x }{x(x+3)} = \dfrac{1}{2}}}$

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$\sf : \implies\: {\bold{ \dfrac{2x + 3 }{x^2 + 3x } = \dfrac{1}{2}}}$

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$\sf : \implies\: {\bold{ 2 ( 2x + 3 ) = x^2 + 3x }}$

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$\sf : \implies\: {\bold{4x + 6 = x^2 + 3x}}$

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$\sf : \implies\: {\bold{ -x^2 + 4x - 3x + 6 = 0 }}$

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$\sf : \implies\: {\bold{ -x^2 + x + 6 = 0 }}$

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• Using quadratic equation

$\sf\implies -x^2 + x + 6 = 0$

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compare the eq with $\sf{\underline{\bold{ax^2 + bx + c = 0 }}}$

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☯ a = -1

☯ b = 1

☯ c = 6

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now :-

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$\sf{\underline{\boxed{\pink{\large{\mathfrak{x = \dfrac{ - b \pm \sqrt D }{2a }}}}}}}$

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$\sf{\underline{\boxed{\pink{\large{\mathfrak{ D = b^2 - 4ac }}}}}}$

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• finding value of D.

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$\sf\implies D = b^2 - 4ac$

$\sf\implies D = (1)^2 - 4 \times -1 \times 6$

$\sf\implies D = 1 + 24$

$\sf\implies D = 25$

$\sf{\underline{\boxed{\blue{\large{\bold{ D = 25}}}}}}$

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putting values in the eq.

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$\sf\implies x = \dfrac{ -b \pm\sqrt D }{2a}$

$\sf\implies x = \dfrac{ -(1) \pm\sqrt {25} }{2\times -1 }$

$\sf\implies x = \dfrac{ 1 \pm 5 }{2}$

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✒$\sf x = \dfrac{ 1 + 5 }{ 2 }$

$\implies x = \dfrac {6}{2}$

$\implies x = 3$

$\sf{\underline{\boxed{\purple{\large{\bold{ x = 3 }}}}}}$

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✒$\sf x = \dfrac{ 1 - 5 }{ 2 }$

$\implies x = \dfrac {-4}{2}$

$\implies x = -2$

$\sf{\underline{\boxed{\purple{\large{\bold{ x = -2 }}}}}}$

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$\sf{\underline{\boxed{\purple{\large{\bold{ x = -2 \: or \:-3 }}}}}}$

• Since days cannot be in negative

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Therefore value of x = 3

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Vivek will take = x days = 3 days

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Yogesh will take = x + 3 days = 3 + 3 days = 6 days

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$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

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• Vivek will take 3 days and Yogesh will take 6 days .