Time and Work :

1. A alone can do a piece of work in 12 days, while working alone B can do the same work in 24 days. If both of them work together, then how many days, the work will finished?

Solution: Here, X=12 and Y=24

∴ Working together, A and B will complete the work in

= XY/X+Y Days= 12 × 24/ 12+24

= 288/36

= 8 days.

2. A, B, and C can complete a piece of work in 10, 15 and 18 days, respectively. In how many days would all of them complete the same work working together?

Solution: Here, X=10, Y=15 and Z=18

∴ The work will be completed in

= XYZ/XY+YZ+ZX days

= 10×15×18/10×15+15×18+18×10 days,

i.e. 2700/600 or, 4.5 days.

3. A and B working together take 30 days to complete a piece of work. If A alone can do this work 10 days, how long would B take to complete the same work?

Solution: Here, X=30 and Y=10

∴ B alone will complete the work in

= XY/Y−X days

= 30×10/30−10

i.e. 300/20=15 days.

4. Ram and Shyam can do a piece of work in 12 days, Shyam and Jodhu in 15 days, Jodhu and Ram in 20 days. How long would each take separately to do the same work?

Solution: Here, X=12, Y=15 and Z=20

∴ A alone can do the work in

=2XYZ/XY+YZ−ZX

=2×12×15×20/12×15+15×20−20×12 days

Or, 7200/240, i.e. 30 days.

B alone can do the work in

=2XYZ/YZ+ZX−XY days

= 2×12×15×20/15×20+20×12−12×15

Or, 7200/360, i.e. 20 days

C alone can do the work in

=2XYZ/ZX+XY−YZ days

= 2×12×15×20/20×12+12×15−15×20

Or, 7200/120, i.e.60 days

5. Sudipto Saha can do a piece of work in 48 days. If Babu Saha works twice as first as Sudipto Saha, how long would they take to finished the work working together.

Solution: Here, X=24 and k=2

∴ Time taken by Sudipto Saha and Babu Saha, working together, to complete the work.

=( X/1+k) days

= (48/1+2) days, i.e. 16 days