sam takes 24 days more than peter to complete a task.sam and peter start working on the task simultaneously and peter leaves 24 days before the task is completed .peter completes 40% of the overall task.how long will peter take to complete the work independently?

Hi,
Suppose Peter can do the work in a days, which means Sam can do it in a+24 days. Assume that task is completed in b days. This means both of them worked together for (b-24) days, as Peter left 24 days before the task is completed. Remaining 24 days Sam worked alone.
this makes the equation,

$$(b-a)*(\frac{1}{a}+\frac{1}{a+24})+\frac{24}{a+24}=1$$ Eq-1
Since peter completes 40% of work that means,
$$\frac{b-24}{a}=0.4$$
which means, b=24+0.4a
Put this in Eq1
$$0.4a*(\frac{1}{a}+\frac{1}{a+24})+\frac{24}{a+24}=1$$
on solving, you will get
$$0.6=(\frac{0.4a+24}{a+24})$$
On further calculation, you will get a=48 which is the answer