Time and work Problems can be solved in Two ways
- Percentage Method
- LCM Method
LCM method is easier to use so will practice by LCM method
Model-1
1.A alone can finish work in 12 days and B alone can finish the same work in 24 days. then in how many days can A and B together will finish same Work?
Ans)
A=12 days A+B=?
B=24 days
Now take the LCM of A and B because we need find out A+B
So LCM of A and B is =24 it means Total work is 24 Units
Now we can find one days work for A and B Seperately
- A=(Total number of units/No of Days)
=(24/12)
=2 units/day
- B=(Total number of units/No of Days)
=(12/12)
= 1 Unit/day
So that A+B's One day's Work= 2+1
=3 units / Day
- A and B together will finish same Work=(Total no.of Units/(No.of units/day))
=24/3
= 8 Days required to complete same job
2.A and B can do a piece of Work in 12 days. While B alone can finish it in 30 days then A alone finish the work in?
Ans)
A+B=12 days A=?
B=30 days
Now take the LCM of (A+B) and B because we need find out A
So LCM of A and B is =24 it means Total work is 60 Units
Now we can find one days work for (A+B) and B Seperately
- A+B=(Total number of units/No of Days)
=(60/12)
=5 units/day
- B=(Total number of units/No of Days)
=(60/30)
= 2 Unit/day
So that B's One day's Work= ((A+B)'s work-A's Work) = (5-3)
=3 units / Day
- B alone can finish same Work=(Total no.of Units/(No.of units/day))
=60/3
= 20 Days required to complete same job
