A and B can complete work together in 5 days.
IfA works at twice his speed and B at half of his
Answers
Answer:
ANSWER
Let A's one day work be
x
1
and B's one day work
y
1
.
It is given that A and B can complete work together in 5 days, therefore, we have:
A+B=
x
1
+
y
1
=
5
1
⇒
xy
y
+
xy
x
=
5
1
⇒
xy
y+x
=
5
1
⇒5(x+y)=xy.....(1)
A worked at twice his speed means
x
2
B worked at half of his speed means
2y
1
Together they complete work in 4 days, therefore, we have:
x
2
+
2y
1
=
4
1
⇒
2xy
4y
+
2xy
x
=
4
1
⇒
2xy
4y+x
=
4
1
⇒4(x+4y)=2xy
⇒2(x+4y)=xy
⇒2x+8y=xy.....(2)
Substitute equation 2 in 1:
5x+5y=2x+8y
⇒5x−2x=8y−5y
⇒3x=3y
⇒x=y
x=y means that number of days worked by A alone is equal to B alone.
Now, substitute the value in equation 1:
x
1
+
x
1
=
5
1
⇒
x
1+1
=
5
1
⇒
x
2
=
5
1
⇒x=5×2
⇒x=10
Hence, it would take 10 days for A alone to complete the job.
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