Question

A takes 6 days less than B to do a work. If both A and B working together can do it in 4 days, how many
days will B take to finish it ?
​

Answer 1

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We call the time it takes for B to finish the piece of work = x

So , work can be done in 1 day = ?

1/x + 1/x-6 = 1/4

x-6 / x(x-6) + x / x(x-6) = 1/4

4(x-6+x) = x² - 6x

4( 2x - 6) = x² - 6x

8x - 24 = x² - 6x

0 = x² - 14x + 24

x = ( x - 12 ) ( x - 2 )

x = 12 and 2

If the time it takes B = 2 days then

the time it takes A = 4 days

:. It would take B a period of 12 days to finish the job .

Answer 2

Answer:

Step-by-step explanation:

Solution:-

Let B complete work in x days.

And A takes x - 6 days to complete it.

According to the Question,

⇒ 1/(x - 6) + 1/x = 1/4

⇒ x + x - 6/x(x - 6) = 1/4

⇒ 4(2x - 6) = 2(x - 6)

⇒ 8x - 24 = x² - 6x

⇒ x² - 14x + 24 = 0

⇒ x² - 12x - 2x + 24 = 0

⇒ x(x - 12) - 2(x - 12) = 0

⇒ (x - 2) (x - 12) = 0

⇒ x = 2, 12 (Neglecting x = 2 as A takes x - 6 days)

⇒ x = 12

Hence, B takes 12 days to complete the work.

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