  # Time and Work - Aptitude Questions and Answers - RejinpaulPlacement

@ : Home > Arithmetic Aptitude > Time and Work > Level - 1 1.
Worker A takes 8 hours to do a job. Worker B takes 10 hours to do the same job. How long should it take both A and B, working together but independently, to do the same job? [IGNOU 2003]

Solution:   A's 1 hour's work = 1/8
B's 1 hour's work = 1/10

(A + B)'s 1 hour's work = (1/8 + 1/10) = 9/40

Both A and B will finish the work in 40/9 = 4   4/9 days. 2.
A and B together can complete a piece of work in 4 days. If A alone can complete the same work in 12 days, in how many days can B alone complete that work? [Bank P.O. 2003]

Solution:   (A + B)'s 1 day's work = 1/4
A's 1 day's work = 1/12
B's 1 day's work = (1/4 - 1/12) = 1/6

Hence, B alone can complete the work in 6 days. 3.
A can do a piece of work in 7 days of 9 hours each and B can do it in 6 days of 7 hours each. How long will they take to do it, working together 8   2/5 hours a day?

Solution:   A can complete the work in (7 * 9) = 63 hours.
B can complete the work in (6 * 7) = 42 hours.

A's 1 hour's work = 1/63
B's 1 hour's work = 1/42

(A + B)'s 1 hour's work = (1/63 + 1/42) = 5/126

Both will finish the work in (126/5) hrs.

Number of days of 8 2/5 hrs each = (126/5 * 5/42) = 3 days. 4.
A and B can do a piece of work in 18 days, B and C can do it in 24 days; A and C can do it in 36 days. In how many days will A, B and C finish it, working together and separately?

Solution:   (A + B)'s 1 day's work = 1/18
(B + C)'s 1 day's work = 1/24
(A + C)'s 1 day's work = 1/36
Adding, we get: 2 (A + B + C)'s 1 day's work = (1/18 + 1/24 + 1/36) = 9/72 = 1/8

(A + B + C)'s 1 day's work = 1/16.

Thus, A, B and C together can finish the work in 16 days.

Now, A's 1 day's work = [(A + B + C)'s 1 day's work] - [(B + C)'s 1 day's work] = (1/16 - 1/24) = 1/48.

A alone can finish the work in 48 days.
Similarly, B's 1 day's work = (1/16 - 1/36) = 5/144
B alone can finish the work in 144/5 = 28 4/5 days

C's 1 day's work = (1/16 - 1/18) = 1/144
C alone can finish the work in 144 days. 5.
A is twice as good a workman as B and together they finish a piece of work in 18 days. In how many days will A alone finish the work?

Solution:  (A's 1 day's work) : (B's 1 day's work) = 2 : 1
(A + B)'s 1 day's work = 1/18
Divide 1/18 in the ratio 2 : 1
A's 1 day's work = (1/18 * 2/3) = 1/27

Hence, A alone can finish the work in 27 days. 6.
A can do a certain job in 12 days. B is 60% more efficient than A. How many days does B alone take to do the same job?

Solution:   Ratio of times taken by A and B = 160 : 100 = 8 : 5
Suppose B alone takes x days to do the job.

Then, 8 : 5 :: 12 : x
=> 8x = 5 * 12
=> X = 7   1/2 days 7.
A can do a piece of work in 80 days. He works at it for 10 days and then B alone finishes the remaining work in 42 days. In how much time will A and B, working together, finish the work? 