1. If A can do a piece of work in x days and B can do the same work in y days then time taken by (A + B) to complete the work = xy / (x + y) days
Q. A can do a piece of work in 10 days and B can do the same work in 12 days. How long will they take to finish the work, if both work together?
Solution
Here x = 10, y = 12
Therefore number of days taken by A and B
= 10 × 12 / (10 + 12)
= 120 / 22
= 60/11 days
2. If A can do a piece of work in x days, B can do the same work in y days and C can do the same work in z days then time taken by (A + B + C) to complete the work
= xyz / (xy + yz + zx) days
Q. If A can do a piece of work in 4 days, B can do the same work in 8 days and C can do the same work in 12 days, then working together, how many days will they take to complete the work?
Solution
Here x = 4, y = 8, z = 12
Therefore number of days taken by ( A+ B+ C)
= 4 × 8 × 12 / (4 × 8 + 8 × 12 + 12 × 4)
= 32 × 12 / ( 32 + 96 + 48)
= 384 / 176
= 24 / 11
3. If A and B can complete a work in x days and A alone can finish that work in y days, then number of days required to complete the work by B = xy / (y - x) days
Q. A and B together can do a piece of work in 12 days and A alone can do it in 18 days. In how many days can B alone do it?
Solution
Here x = 12, y = 18
Time taken by B = 12 × 18/ (18 - 12)
= 36 days
4. If A can do a work in x days and B can do y% fast than A, then B will be complete the work in 100x / (100 + y) days
Q.Kamal can do a work in15 days and Vimal is 50% more expert than Kamal to complete the same work, then find total time taken to complete the work by Vimal.
Solution
Here x = 15, y = 50%
Now, time taken by Vimal = 100x / (100 + y)
= 100 × 15 / (100 + 50)
= 1500 / 150
= 10 days
5. A and B do a piece of work in a and b days, respectively. Both begin together but after some days, A leaves off and the remaining work is completed by e in x days. Then, the time after which A left, is given by T = (b - x) a / (a + b)
Q. A and B can do a piece of work in 40 days and 50 days, respectively. Both begin together but after a certain time, A leaves off. In this case B finishes the remaining work in 20 days. After how many days did A leave?
Solution
Here a = 40, b = 50, x = 20, T =?
T = ( 50 - 20) × 40 / ( 40 + 50)
= 30 × 40 / 90
= 40 / 3 days
Q. A and B together can do a piece of work in 12 days, while B alone can finish it in 30 days. A alone can finish the work in [SSC (10+2) 2012]
Solution
Here x = 12, y = 30
Required number of days
= 12 × 30/(30 - 12)
= 360 / 18
= 20 days
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