107. X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?

✅ The correct answer is option B.
Work done by X in 4 days =

1
x 4

=
1
.

20
5

Remaining work =

1 –
1

=
4
.

5
5

(X + Y)’s 1 day’s work =

1
+
1

=
8
=
2
.

20
12
60
15

Now,
2
work is done by X and Y in 1 day.

15

So,
4
work will be done by X and Y in

15
x
4

= 6 days.

5
2
5

Hence, total time taken = (6 + 4) days = 10 days.