Question

Answer the question of the above attachment !

Class level : 10

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Answer 1

★ Answer

• A takes 6 days less than B to complete work.
• Both A and B can complete work in 4 days

Let B complete his work in x days.

As, One day work of B,

→ 1/x

again, As We know that A takes 6 days less than B to complete any work, One day work of A,

→ 1/(x-6)

According to Question,

→ 1/x + 1/(x-6) = 1/4

→ x-6+x/x(x-6) = ¼

→ 2x-6/x²-6x = 1/4

→ 8x-24 = x² - 6x

→ x²-6x-8x+24 = 0

→ x² - 14x + 24 = 0

→ x² -(12+2)x+24 = 0

→ x²-12x-2x + 24 = 0

→ x(x-12) -2(x-12) = 0

→ x = 12, 2

Finally, Both the values are Positive means that Both are acceptable. but if B takes 2 days to complete work then A takes Negative days to complete work. therefore we accept 12 days that B takes to complete work.

Verification:

→ 1/12 + 1/(12-6) = 1/4

→ 1/12 + 1/6 = 1/4

→ 1+2/12 = 1/4

→ 3/12 = 1/4

→ 1/4 = 1/4

Hence, B takes 12 days to complete work.

Answer 2

Given : A takes 6 days less than B to do the work & If both A and B working together can do it in 4 days.

To Find : Find howmany days will B to finish it ?

_________________________

Solution : Let B complete his work in x days.

• One day work of B

• ${\sf{\dfrac{1}{x}}}$

$~$

$\underline{\frak{As ~we ~know ~that~:}}$

• A takes 6 days less than B to complete any work, One day work of A

• ${\sf{\dfrac{1}{\bigg(x~-~6\bigg)}}}$

$~$

$\pmb{\frak{\underline{According ~to~ the ~Given ~Question~:}}}$

$~$

${\sf\qquad\qquad:\implies{\dfrac{1}{x}~+~\dfrac{1}{\bigg(x~-~6\bigg)}~=~\dfrac{1}{4}}}$

${\sf\qquad\qquad:\implies{\dfrac{x~-~6~+~x}{x}~-~\bigg(x~-~6\bigg)~=~\dfrac{1}{4}}}$

${\sf\qquad\qquad:\implies{\dfrac{2x~-~6}{x^2~-~6x}~=~\dfrac{1}{4}}}$

${\sf\qquad\qquad:\implies{8x~-~24~=~x^2~-~6x}}$

${\sf\qquad\qquad:\implies{x^2~=~6x~-~8x~+~24~=~0}}$

${\sf\qquad\qquad:\implies{x^2~=~14x~+~24~=~0}}$

${\sf\qquad\qquad:\implies{x^2~-~\bigg(12~+~2\bigg)~x~+~24~=~0}}$

${\sf\qquad\qquad:\implies{x^2~-~12x~-~2x~+~24~=~0}}$

${\sf\qquad\qquad:\implies{x(x~-~12)~-~2\bigg(x~-~12\bigg)~=~0}}$

$\qquad\qquad:\implies{\underline{\boxed{\frak{\pink{x~=~12~\&~2}}}}}$★

$~$

Henceforth,

• Both the values are Positive means that Both are acceptable. but of B takes 2 days to complete work then A takes Negative days to complete work. $\bf\therefore$we accept 12 days that B takes to complete work.

$~$

Hence,

$\therefore\underline{\sf{B~takes~\bf{\underline{12~days}}~\sf{to~complete~work}}}$

$~$

________________________

V E R I F I C A T I O N :

$\qquad\qquad{\rm\dashrightarrow{\dfrac{1}{12}~+~\dfrac{1}{(12~-~6)}~=~\dfrac{1}{4}}}$

$\qquad\qquad{\rm\dashrightarrow{\dfrac{1}{12}~+~\dfrac{1}{6}~=~\dfrac{1}{4}}}$

$\qquad\qquad{\rm\dashrightarrow{\dfrac{1~+~2}{12}~=~\dfrac{1}{4}}}$

$\qquad\qquad{\rm\dashrightarrow{\dfrac{3}{12}~=~\dfrac{1}{4}}}$

$~~~~~~~~~~~~~~~~\dashrightarrow\large\pmb{\frak\red{\dfrac{1}{4}~=~\dfrac{1}{4}}}$