SOLUTION: Adil can do a job alone in 9 days while Babar can do it alone in 15 days Adil works alone on the job for x days after which Babar takes over and finishes the remainder of the job i

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Question 1127014: Adil can do a job alone in 9 days while Babar can do it alone in 15 days Adil works alone on the job for x days after which Babar takes over and finishes the remainder of the job in 10 days find the value of x?
Found 3 solutions by josmiceli, greenestamps, ikleyn:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Adil's rate of working:
[ 1 job ] / [ 9 days ]
Babar's rate of working :
[ 1 job ] / [ 15 days ]
-----------------------------
Let +y+ = fraction of job that Adil completes
in +x+ days
+1%2F9+=+y%2Fx+
multiply both sides by +9x+
+x+=+9y+
+y+=+%281%2F9%29%2Ax+
Adil completes +%281%2F9%29%2Ax+ of the job, so +%288%2F9%29%2Ax+
of the job is left
----------------------
Barbar does +%288%2F9%29%2Ax+ of the job in 10 days, so
+1%2F15+=+%28%288%2F9%29%2Ax%29+%2F+10+
Multiply both sides by +150+
+10+=+15%2A%288%2F9%29%2Ax+
+90+=+120x+
+x+=+3%2F4+
-------------------
Get a 2nd opinion if you can


Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


I got lost trying to figure out the solution by the other tutor....

The problem is solved MUCH more easily if you start by figuring out the fraction of the job Babar does.

He takes 15 days to do the job alone; in the 10 days he worked, the fraction of the job he did was 10/15 = 2/3.

That means Adil did 1/3 of the job.

Since Adil would take 9 days to do the whole job alone, the number of days he worked to do 1/3 of the job was 9/3 = 3 days.

ANSWER: Adil worked on the job for 3 days.

Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.
Working for x days, Adil made  x%2F9  parts of the entire job.


Working 10 days,  Babar made  10%2F15  parts of the entire job.


It gives you an equation to find x:


    x%2F9 + 10%2F15 = 1.


From the equation,


    x%2F9 = 1 - 10%2F15 = 1 - 2%2F3 = 1%2F3,


hence


    x = 9%2A%281%2F3%29 = 3 days       Answer