Two workers Anushka and Kriya working together completed a job in 4 days. If Anushka worked two-third times as efficiently as she actually did and Kriya worked one-sixth as efficiently as she actually did, the work would have been completed in 8 days. To complete the job alone, Anushka would require
Two workers Anushka and Kriya working together completed a job in 4 days. If Anushka worked two-third times as efficiently as she actually did and Kriya worked one-sixth as efficiently as she actually did, the work would have been completed in 8 days. To complete the job alone, Anushka would require
1). 12 days
2). 6 days
3). 8 days
4). 9 days
1 answers
Let number of days needed by Anushka and Kriya to finish the work be x and y respectively.
∴ part of work done by Anushka in one day = 1/x
And part of work done by Kriya in one day = 1/y
∴ Part of work done by both of them working together $(= \;\frac{1}{x} + \frac{1}{y} = \frac{1}{4})$ -------(i)
According to the question, if Anushka worked (2/3) as efficiently as she actually did,
Part of work done by Anushka in one day = 2/3x
Also, Kriya worked (1/6) as efficiently as she actually did,
∴ Part od work finished by Kriya in one day = 1/6y
In this case, the work would have been completed in 8 days.
$(\therefore \frac{2}{{3x}} + \frac{1}{{6y}} = \frac{1}{8})$ ---------(ii)
Solving equation (i) and (ii) simultaneously, we get
⇒ x = 6
∴ Anushka would require 6 days to complete the job alone.