Q9 of 227 Page 107

A takes 6 day less than the time taken by B to finish a piece of work. If both A and B together can finish it in 4 days, find the time that B would take to finish this work by himself.

Let x be the tune taken by A to finish the work.


So, x – 6 be the time taken by B to finish the work.


Work done by A in one day =


Work done by B in one day =


Number of days taken by both to finish the work =



⇒


⇒


⇒ 4(2x – 6) = x2 – 6x


⇒ 8x – 24 = x2 – 6x


⇒ x2 – 6x – 8x + 24 = 0


⇒ x2 – 14x + 24 = 0


⇒ x2 – 12x – 2x + 24 = 0


⇒ x(x – 12) –2(x – 12) = 0


⇒ (x – 12)(x – 2) = 0


x – 12 = 0 or x – 2 = 0


x = 12 or x = 2


Here, 2 is not admissible.


So, B is taking 12 days to finish the work.


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x2 – 8x + 12 = 0