Time and Work part is one of the important topics included in the Quantitative Aptitude section of all Bank and SSC examinations. These topics will earn you 2-3 marks. A thorough understanding of concepts will really help you to answer all the questions from this part. Aspirants always have to practice a large number of questions in order to understand how to approach, different question patterns, improve speed and accuracy of answers. In this article attempt various Time and Work questions.
Concepts and Tricks to solve Time and Work Questions for Bank, SSC, RRB exam.
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Time and Work Questions for Bank and SSC Exams
Firstly, let us practice some questions with detailed solutions:
1. A takes 8 hours to do work. And that of B takes 10 hours to do the same. How long should it take both A and B, working together but independently, to do the same work?
Solution: The answer can be done through TWO methods i.e. Unitary method and L.C.M method`
Unitary method:
A’s 1 day’s work = 1/8
B’s 1 day’s work = 1/10
(A+B) 1 day’s work = (1/8)+(1/10) = 9/40
Therefore, both A and B will complete the work in 40/9 = 4 and 4/9 days.
L.C.M method:
Here the Efficiency is calculated by equation Efficiency (E) = Work (W) / Days (D)
A can do a work in 8 days.
B can do the work in 10 days.
Find out the LCM (that is the total work) of 8 and 10 = 40
So, Efficiency of A = 40/8 = 5
Efficiency of B = 40/10 = 4
So total Efficiency= 5+4 = 9
So the total days D taken by them to complete the work = W/ E = 40/ 9= 4 and 4/9 days.
Shortcuts to find Squares and Square-roots.
2. Ram does a work in 10 days and Nitu does the same work in 15 days. In how many days they together will do the same work?
Solution:
Efficiency (E) = Work (W) / Days (D)
Ram can do a work in 10 days.
Nitu can do the work in 15 days.
Find out the LCM (that is the total work) of 10 and 15 = 30
So, Efficiency of Ram = 30/10 = 3
Efficiency of Nitu = 30/15 = 2
So total Efficiency= 3+ 2= 5
So the total days taken by them to complete the work together = W/ E = 30/ 5= 6 days.
3. A and B together can complete a particular task in 4 days. If A alone can complete the same task in 12 days. How many days will B take to complete the task if he works alone?
Solution:
A and B can do a work in 4 days.
A can do the work alone in 12 days.
Shortcut Formula: If A and B together can do a piece of work in x day and A alone can do it in y days, then B alone can do the work in:
x y / y – x days
Then,
B alone can do the whole work in:
4 × 12 = 48 / 12- 4= 48/ 8 = 6 days
Shortcuts to find Cubes and Cube-roots.
4. A and B together can complete a work in 40/3 days. B can complete the same work, working alone in 6 more days than A. Find the number of days taken by B to complete the work alone.
Solution:
Given A+ B = 40/3
Let A completes work in ‘a‘ number of days and B alone completes in a+ 6 days.
Let the total work be 40. Then, Efficiency of A+ B = 3.
The efficiency of A = 40/a
The efficiency of B = 40/a+6
Substituting this in Efficiency of A+ B = 3, we will get 3a² -62a – 240 = 0
solve this, then A= 24 days, B = 30 days.
5. Two workers A and B working together completes a work in 5 days. If A worked twice as efficiently ad he actually did and B worked 1/3 as efficiently as he did actually, then the work would have completed in 3 days. Find the time for A to complete the work alone.
Solution:
A+ B = 5 days
2A + 1/3 B = 3 Days
i.e., (A + B) 5 = (2A + B/3) 3 = A/B = 4/1
Efficiency= A + B = 4+ 1 = 5
Work = Efficiency × Days = 5 × 5 = 25
Number of days needed for A to complete the work = W/ E = 25/ 4 = 6 and 1/4 days.
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Now practice more questions on Time and Work:
1. A piece of work is done by 6 men and 5 women in 6 days or 3 men and 4 women in 10 days. In how many days the work can be done by 9 men and 15 women?
a) 5 days
b) 3 days
c) 4 days
d) 2 days
e) none
2. B is 20% more efficient than A. B started the work and did the same for ‘x’ days and then B is replaced by A. A completed the remaining work in ‘x+8’ days. The ratio of work done by A & B is 3:2. In how many days A+B completes the whole work?
a) 11 7/11days
b) 11 3/11 days
c) 17 3/11 days
d) 13 7/11 days
e) none
3. Two pipes A and B can fill a tank in 18 hours and 24 hours respectively, while a 3rd pipe can empty the full tank in 30 hrs. All 3 pipes are opened ar first. After 12 hours pipe C is closed, find time at which the tank is filled completely?
a) 14. 4 hours
b) 13.4 hours
c) 3 hours
d) 6 hours
e) none
4. A and B can do a piece of work in 12 days. A is 4/3 times as efficient as B. In how many days can A alone finish the work?
a) 22 days
b) 31 days
c) 21 days
d) 18 days
e) none
Quantitative Aptitude-Practice Percentage problems.
5. 4 men complete a work in 18 days. 4 women complete the same work in 28 days. In how many days will 9 men and 12 women together complete the same work?
a) 2 2/3
b) 3 4/5
c) 3 3/11
d) 4 4/13 days
e) none
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