abhishek takes 6 days less than the time taken by anubhav to finish a piece of work if both of them together finish the work in 4 days find the time taken by anubhav alone to finish the work
Answers
Answer:
12 days
Step-by-step explanation:
Step -1: Finding the work done by A and B in a day.
Let B takes a total of x days to complete the work alone.
So as know that A takes 6 days less than B we can write that A takes
x - 6 days to complete the work alone.
Work done by B in a day =
x
1
Work done by A in a day =
x−6
1
Step -2: Finding x .
As we know that A and B together complete the work in 4 days,we can write
x
1
+
x−6
1
=
4
1
Taking LCM and solving we get,
x(x−6)
x−6+x
=
4
1
x(x−6)
2x−6
=
4
1
Cross - multiplying we get,
8x−24=x
2
−6x
x
2
−14x+24=0
x
2
−12x−2x+24=0
x(x−12)−2(x−12)=0
x=2,12
We will reject x=2 as x - 6 will become negative.
Hence, B takes 12 days to complete the work alone.