Formulas and Quick Tricks for Time and Work
- If 1/n of a work is done by A in one day, then A will take n days to complete the full work.
- If A can do a piece do a piece of work in X days and B can do the same work in Y days, then both of them working together will do the
same work in XY/(X+Y) days
- If A, B and C, while working alone, can complete a work in X, Y and Z days respectively, then they will together
complete the work in XYZ/(XY+YZ+ZX) days
- If A does 1/nth of a work in m hours, then to complete the full work A will take nxm hours
- If A and B can together finish a piece of work in X days, B and C in Y days and C and A in Z days, then
a) A, B and C working together will finish the job in (2XYZ/XY+YZ+ZX) days.
b) A alone will finish the job in (2XYZ/XY+YZ – ZX) days.
c) B alone will finish the job in (2XYZ/ZX+XY – YZ) days.
d) C alone will finish the job in (2XYZ/ZX+YZ – XY) days.
- If A can finish a work in X days and B is k times efficient than A, then the time taken by both A and B working together to complete the
work is X/(1+k).
- If A and B working together can finish a work in X days and B is k times efficient than A, then the time taken by A working alone to
complete the work is (k+1)X and B working alone to complete the work is (k+1/k)X
Questions and Solved Examples on Time and Work
Q.1: A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is:
A. 1/4
B. 1/10
C. 7/15
D. 8/15
Answer: D. 8/15
Explanation: A's 1 day's work = 1/15
B's 1 day's work = 1/20
(A + B)'s 1 day's work = (1/15 + 1/20) = 7/60
(A + B)'s 4 day's work = (7/60 * 4) = 7/15
Therefore, Remaining work = (1 – 7/15) = 8/15
Q.2: Kim can do a work in 3 days while David can do the same work in 2 days. Both of them finish the work together and get Rs. 150. What is the share of Kim?
A. Rs. 50
B. Rs. 60
C. Rs. 70
D. Rs. 80
Answer: B. Rs. 60
Explanation: Kim's wages : David's wages = Kim's 1 day work : David's 1 day work = 1/3 : 1/2 = 2:3
Kim's share = 2/5 * 150 = Rs. 60
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Q.3: Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is?
A. 15 days
B. 16 days
C. 17 days
D. 18 days
Answer: B. 16 days
Explanation: Ratio of times taken by Sakshi and Tanys = 125:100 = 5:4
Suppose Tanya takes x days to do the work.
5:4 :: 20:x
=> x = 16 days
Hence, Tanya takes 16 days to complete the work.
Q.4: 12 Men or 18 women can reap a field in 14 days. The number of days that 8 men and 16 women will take to reap it?
A. 7 days
B. 8 days
C. 9 days
D. 10 days
Answer: C. 9 days
Explanation: 12 men = 18 women or 1 man = 3/2 women
Therefore 8 men + 16 women = (8 × 3/2 + 16) women i.e.., 28 women
Now 18 women can reap the field in 14 days
Therefore, 28 women can reap it in = 9 days
Q.5: A is thrice as efficient as B and is, therefore, able to finish a piece of work 10 days earlier than B. In how many days A and B will finish it together?
A. 3 days
B. 4 days
C. 5 days
D. 6 days
Answer: C. 5 days
Explanation: WC = 3:1
WT = 1:3
x ------- 3x
1/x – 1/3x = 1/10
x = 20/3
3/20 + 1/20 = 1/5 => 5 days
Q.6: A work which could be finished in 9 days was finished 3 days earlier after 10 more men joined. The number of men employed was?
A. 18 men
B. 20 men
C. 22 men
D. 24 men
Answer: B. 20 men
Explanation: x ------- 9
(x + 10) ---- 6
x * 9 = (x + 10)6
x = 20
Q.7: Tina can do a certain job in 12 hours. Working independently, Ann can do the same job in 9 hours. If Tina Works independently at the job for 8 hours and then Ann works independently, how many hours will it take Ann to complete the remainder of the jobs?
A. 2/3 hr
B. 3/4 hr
C. 1 hr
D. 3 hrs
Answer: D. 3 hrs
Explanation: Work done by Tina in 1 hr = 1/12
Work done by Tina in 8 hrs = 1/12*8 which is 2/3
Now, the remaining work is 1/3 which is completed by Ann in 1/3*9 which is 3 hrs
Q.8: A can do a piece of work in 40 days; B can do the same in 30 days. A started alone but left the work after 10 days, then B worked at it for 10 days. C finished the remaining work in 10 days. C alone can do the whole work in?
A. 16 days
B. 24 days
C. 32 days
D. 40 days
Answer: B. 24 days
Explanation: 10/40 + 10/30 + 10/x = 1
x = 24 days
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Q.9: Ravi can do a piece of work in 30 days while Prakash can do it in 40 days. In how many days will they finish it together?
A. 16 4/11 days
B. 17 1/7 days
C. 23 2/7 days
D. 27 1/7 days
Answer: B. 17 1/7 days
Explanation: 1/30 + 1/40 = 7/120
120/7 = 17 1/7 days
Q.10: Varma can read a book in k minutes. What part of the book can he read in 8 minutes? Given (k>8)
A. k+8
B. 8/k
C. k/8
D. (k-8)/k
Answer: B. 8/k
Explanation: Part of the book he can read in 1 minute = 1/k
Part of the book he can read in 8 minutes = 8/k