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CBSE Class 8 Answered

Three friends, X, Y and Z complete the work in x days, (x+5) days and 12 days respectively. they started to work together but X left the work after 2 days and just left the work one day before the completion of the work. if the total work completed in (53/9) days, then find the value of x. Answer is -->10  (solve + explain)
Asked by jhajuhi19 | 09 Oct, 2023, 09:24: PM
answered-by-expert Expert Answer
straight X space takes space straight x space days space to space complete space one space work
hence space in space one space day space straight X thin space completes space 1 over straight x space work
similarly
straight Y space completes space fraction numerator 1 over denominator straight x plus 5 end fraction space work space in space one space day
and
straight Z thin space completes 1 over 12 space work space in space one space day

Now space work space is space completed space in space 53 over 9 days

straight Y space works space for space 53 over 9 days space so space work space done space in space total space by space straight Y space equals fraction numerator 1 over denominator straight x plus 5 end fraction cross times space 53 over 9
straight Z space works space for space open parentheses 53 over 9 minus 1 close parentheses days comma space hence space total space work space done space by space straight Z space equals space 1 over 12 cross times open parentheses 53 over 9 minus 1 close parentheses
straight X space works space for space 2 space days comma space hence space total space work space done space by space straight X space equals space 2 over straight x

Together space they space complete space one space work
fraction numerator 1 over denominator straight x plus 5 end fraction cross times space 53 over 9 plus 1 over 12 cross times open parentheses 53 over 9 minus 1 close parentheses plus 2 over straight x equals 1

Solving space we space get space straight x space equals space 10.
Answered by Arun | 17 Oct, 2023, 08:48: AM
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