Simplest way to solve work and time problems. We are telling you how to solve work and time problems easily in competition exam like SSC, IBPS, SBI Clerk /PO, RBI, GATE, CAT, State PCS, Job interviews etc. With these short and accurate trick you can easily solve these type of work and time problems.Mostly three type of work and time problem asked in the competition. Let’s start with example one by one.
Time and work problem type #1
If A completed a work in 6 days and B completed that work in 4 days then how much time they both take to complete that work together.
This is a simple type of work and time problem. And to solve this problem we have to follow these steps
(1) Find the work done by A in one day
(2) Find the work done by B in one day
(3) Find work done by A and B together in one day
(4) Find the total time taken by A and B together
Now let’s start
Work done by A in one day is 1/6 or 100/6 = 16.67 %
work done by B in one day is 1/4 or 100/4 = 25 %
work done by A and B together is 1/6 + 1/4 or 5 /12 = 41.67
Now time taken to complete work together = 100/41.67 = 2.39 days or 2.4 days
Now you can solve this question in one step = 1/(time taken by A in one day + time taken by B in one day) = 1 / ( 1/6 + 1/4) = 12/5 = 2.4 days
Time and work problem type #2
Another type of work and time problem is, A can do work x time more than B. In this type of comparison you can use simple calculation to solve.
Ratio of work done for same work by A and B is = x : 1
Ratio of time taken by A and B is = 1 : x
Now you can easily calculate the work by A or B in one day and then you can solve the question very easily.
Time and work problem type #3
If three persons are given then how to solve work and time problem. Let’s take an example
If (A + B) can complete a piece of work in 14 days. (B+C) complete the 1 /7 work in one day. ( C+A) complete 1/8 part of work in one day then how much time they all take together to complete this work.
Now (A+B ) do work in one day = 1/14 .
A + B = 1 / 14
B + C = 1 / 7
C + A = 1 / 8
Now add the all three and we get
(A+B) + (B + C) + ( C + A) = 1/14 + 1/7 + 1/8
2(A+B+C) = (14×7)+(8×7)+(8 ×14)/ 14 × 7 × 8
2(A+B+C) = 98 + 56 + 112/ 784
(A+B+C) = 0.169
All three can complete 0.169 part of work in one day.
Total time taken by three is = 1 / .169 = 5.91 days
Time and work problem type #4
If A and B completes a work in x hour or days. A alone takes “y” more hours or days . A alone takes “z” more hours or days. Then A and B both will complete this work in = √(y×z) days or hours.
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Example : If A and B assigned to complete a task. A alone take 8 more hours and B alone takes 9/2 hours. Then How much time both A and B will take to complete this task.
Let A and B can complete this task in = x hours.
Work by A and B in one hour = 1/x …..(i)
A alone can complete this task = x + 8 hours
Work by A in one hour = 1 / ( x + 8 ) ……(ii)
B alone can complete this task = x + 9/2
Work by B in one hour = 1 / (x + 9/2 ) ……(iii)
So, Work done by A and B in 1 hour = Work by A in one hour + Work by B in one hour
1/x = {1 / ( x + 8 ) }+ {1 / (x + 9/2 )}
After solving this you will get x = 6 .
Now use short trick = √ (8 × 9 / 2) = √36 = 6.
Try this trick on other questions like this.
Time and work problem type #5
Another Work and time problem is Tank filling rate and time. Let’s take an example
If a pipe filled tank in 40 min and a hole in bottom drained the water in 80 min. Then how much time it will take to fill the tank.
In this problem we have a pipe that can fill the tank in 40 min and another hole in the bottom of the tank that empty the tank in 80 min. To calculate the time required to fill tank, we have to first calculate the efficiency of filling and draining of water. Then subtract the efficiency of draining from efficiency of filing and after that divide that with 100. Let’s see this step by step
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Efficiency of filling = 100/40 = 2.5%
Efficiency of draining = 100/60= 1.67 %
Total efficiency of filling tank = 2.5-1.67 = 0.83 %
time required to fill tank = 100/0.83 = 120.48 min.
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