Question

A can do s piece of work in 'x' days and B can do the same work in (x + 16) days. If both working together can do it in 15 days. Calculate 'x'
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Answer 1

Given A do a piece of work in x days and B do work in x+16 days

Then A one day work =

x

1

days

AND B one day work =

x+16

1

days

Then Both one day work =

x

1

+

x+16

1

=

x(x+16)

x+16+x

=

x

2

+16x

2x+16

So both do work in

2x+16

x

2

+16x

days

But both do work in 15 days

∴

2x+16

x

2

+16x

=15

⇒x

2

+16x=30x+240

⇒x

2

−14x−240=0

⇒x

2

−24x+10x−240=0

⇒x(x−24)+10(x−24)=0

⇒(x−24)(x+10)=0

Then x−24=0,x=24

And x+10=0,x=−10

But work done is not negative

Then work done =24 days