After how many days did Akbar join Ajay given that Akbar can do a piece of work in 40 days and Ajay can do a piece of work in 60 days.Akbar works on the piece of work alone for some days.Then Ajay joins him and together they complete the work for 10 days earlier than the time Akbar alone would have taken.
options given:
a) 30 b)40) c)15 d)19
My Approach:
Akbar $1$ day efficiency=$2.5$%
Ajay $1$ day efficiency=$1.66$%
Together Their $1$ day work efficiency is $4.16$%
This means they can together complete in $24$ days.But given they took $30$ days together(as $40$-$10$=$30$)
(Also $40$ because Akbar alone took it and subtract $10$ as specified)
I could not solve after this step.
Best Answer
Suppose Ajay joins Akbar after $d$ days. This means that on each of those $d$ days, $\frac{1}{40}$ of a piece of work was done, and on each of the remaining $30-d$ days, $\frac{1}{40} + \frac{1}{60} = \frac{5}{120}$ was done. The total is supposed to be $1$. This means that:
$\frac{1}{40}\cdot d + \frac{5}{120}\cdot(30-d) = 1$.
Can you take it from there?