Time and Work Problems ( Level 1)

Problems on Time and Work

A is twice as good a workman a B and therefore A takes 6 days less than B to finish the work individually. If A and B working together complete the work in 4 days, then how many days are required by B to complete the work alone?
Solution:
   A B
Efficiency        2 : 1
Days                1     : 2
(Days x 1/Efficiency)
Now, let A requires x days, then B requires 2x days.
Therefore difference in number of days (= 2x – x) = x = 6
 X = 6
Therefore  B requires 2X = 2 x 6 = 12 days

Arun can do a piece of work in 20 days. He started the work and left after some days, when 25% work was done. After it aruna joined and completed it working for 10 days. In how many days arun and aruna can do the complete work, working together?
Solution:

Efficiency of arun = 5% = (100/20)
Rest work = 75%
Efficiency of aruna = 75/10 = 7.5%
Combined efficiency of arun and aruna = 12.5% = (7.5+5)
Therefore number of days required by arun and aruna, to work together
100/12.5 = 8 days


A group of workers can complete a job in 120 days. If there were 4 more such workers then the work could be finished in 12 days less. What was the actual strength of workers? 
a) 12 b) 30 c) 50 d) 40
Solution:

Go through options. Consider choice (D)
36 x 120 = 40 x 180
4320 = 4320
Hence choice D is correct

A man, a woman and girl worked for a contractor for the same period. A man is twice efficient as a woman and a woman is thrice efficient as a girl Rs.10000 were given to all of them. What is the sum of money received by a woman and a girl together?  
Solution:

Efficiency of man : woman : girl = 6:3:1
Share of a woman and girl = (3+1) / (6+3+1) x 10,000
= 4/10 x 10000  = rs.4000

A is twice efficient as B and together they do the same work in as much time and C and D together. If C and D can complete the work in 20 and 30 days respectively, working alone, then in how many days A can complete the work individually? 
Solution:
                 A    +     B          =        C    +     D
Ratio of efficiency       10x +   5x 9x    +     6x
                     15x    15x
Therefore ratio of efficiency of A:C = 10:9
Therefore ratio of efficiency of A:C = 9:10
Therefore number of days  taken by A = 18 days

Pipe A can fill an empty tank in 30 hours while B can fill it in 45 hours. Pipe A and B are opened and closed alternatively i.e., first pipe A is opened, then B, again A and then B and so on for 1 hour each time without any time lapse. In how many hours the tank will be filled when it was empty, initially?
Solution:

In one hour pipe A can fill = 1/30 part of the tank
In one hour pipe B ca fill = 1/45 part of the tank
In two hour pipes A and B can fill = 1/18 part of the tank
Therefore in 36 hours the tank will be filled completely filled.