Question

A is a creator and b is a destroyer. a can complete a building in 20 days while b can destroy it in 30 days. if both working alternate days, then after how much time will the building completes for the first time

Answer 1

The building will be completed for the first time in 115 days.

Answer 2

Let the total no. Of work be
LCM(20,30)=60unit.

Then,A can complete building in 20

days , so,he will complete

60/20=3unit/day.

Again,B can destroy the work the in

30days so, he will work 60/-30

= -2unit/day (work is -ve as he had

destroyed).

When they both work alternate,

If A start the work then a 'll make 3u

and very next day B will destroy 2u.


i.e work after 2days =3u-2u=1u.

Again,it will form cycle of 2days .

In 1 cycle 1 unit of work is completed.

And,total work=60u.

So,it will take 60cycles

And ,1cycle=2days

So, They both will take 120 days to
finish.

So, building completes after 120 days

Hope it helps.