Correct option is (d) 22\(\frac 12\) days
Let the amount of work be x.
Now A does the work in 25 days.
∴ In 1 day A does \(\frac x{25}\) work,
B does the work in 20 days.
∴ In 1 day B does \(\frac x{20}\) work,
C does the work in 24 days.
∴ In 1 day C does \(\frac x{24}\) work.
A works for (2 + 3) days = 5 days.
∴ In 5 days A does 5 × \(\frac x{25}\) work = \(\frac x{5}\) work,
B works for 2 days.
∴ In 5 days B does 2 × \(\frac x{20}\) work = \(\frac x{10}\) and
C works for \((2 + 8\frac53 + 3 )\)days = \(\frac{68}5\) days
∴ In \(\frac{68}5\) days C does \(\frac{68}5\) × \(\frac x{24}\) work = \(\frac {17x}{15}\) work.
∴ The total work done by A,B and C, so far = \(\frac x5 +\frac x{10} + \frac{17x}{13}\) work
= \(\frac{13x}{15}\) work
∴ The work left = x − \(\frac{13x}{15}\) work
This work is done by D in 3 days.
∴ D will finish the whole i.e x work in 3 × \(\frac{15}2\) days = 22\(\frac 12\) days.
