X can do 4 of a cetain work 1 in 10 days and Y can do 2 part of the same work in 5 days. In how many days will X and Y together do thrice the same work?
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Answer:
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
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