### 20 Oct

Time and work is one of the most important topics in quantitative aptitude section of Bank PO / Clerk and SSC exams. There are plenty of questions from this topic and you can’t neglect it at any cost. However, the traditional method of solving time and work questions, which used to work pretty well at school level, does not prove to be that effective given the time constraint of a competitive Govt. job exam.

Hence, candidates must use a shortcut based approach which can help them answer all questions without having to mug up any formulae. Discussed below, is a unique approach devised by experts having immense experience of providing Coaching for SSC in DelhiPast year exam questions have been chosen and the use of this approach has been illustrated alongside.

Question- 1 A is twice as good a workman as B and together they are able to complete a piece of work in 18 days. In how many days can A alone finish the work? (A) 25 (B) 27 (C) 28 (D) None of these

Explanation

Ans. (B)

First of all, we have to find the ratio of efficiency {daily work done}. The ratio of efficiency of A: B = 2:1. It is given in the question that A is twice as efficient as B.
This means if B can do 1 unit work daily, then A can do 2 units of work per day. So, A and B can together do 3 units of work per day. They can together do the job in 18 days.
The total work done by A and B is 183 = 54 units. Now if A alone does the work, that means he will have to complete the 54 units of work by himself.
A can complete 54 units of work in = (54/2) = 27 days.

Question- 2 If A and B can do a piece of work in 20 days and 30 days respectively, then in how many days can A and B together complete the work? (A) 50 days (B) 12 days (C) 25 days (D) 12.5 days

Explanation

Ans. (B)

Generally, efficiency of A and B is not given directly in the question.
Here, first of all, we have to assume the total work done to find their efficiency.
Let work done = LCM (20, 30) = 60 units.
If A can do these 60 units in 20 days, he can daily do 3 units.
If B can do these 60 units in 30 days, he can daily do 2 units.
So, in total, they can together do 5 units daily.
Thus, the total work can be done by them in = (60/5) = 12 days

Question- 3 A man can do a piece of work in 5 days, but with the help of his son, he can do it in 3 days. In how much time can the son do the work alone? (A) 6.5 days (B) 7 days (C) 7.5 days (D) 8 days

Explanation

Ans. (C)

Let work done = LCM (5, 3) = 15 units
A man can do this job in 5 days, so his daily work done will be 15/5 = 3 units.
He and his son can together do it in 3 days, so together they can daily do 15/3 = 5 units.
So his son alone can daily do = 5 – 3 = 2 units
Thus, if his son has to do the work alone, he can do it in = 15/2 = 7.5 days

Question- 4 A, B and C can complete a piece of work in 24, 6 and 12 days respectively. Working together, they will complete the same work in (A) 5/7 days  (B) 7/12 days  (C) 7/24 days (D) 24/7 days

Explanation

Ans. (D)

Let work done = LCM (24, 6, 12) = 24 units
If A can do these 24 units in 24 days, he can daily do 1 unit.
If B can do these 24 units in 6 days, he can daily do 4 units.
If C can do these 24 units in 12 days, he can daily do 2 units.
Then, in total, they can together do 7 units daily.
So the total work will be done in = 24/7 days

Question- 5 A can construct a railway track in 16 days. B can construct the same track in 12 days. With the help of C, they did the job in 4 days only. Then, C alone can construct the track in (A) 46/5 days (B) 47/5 days (C) 48/5 days (D) None of these

Explanation

Ans. (C)

Let work done = LCM (16, 12, 4) = 48 units
A can do this job in 16 days, so his daily work done will be 48/16 = 3 units.
B can do this job in 12 days, so his daily work done will be 48/12 = 4 units.
A, B & C can together do it in 4 days. Together they can daily do 48/4 = 12 units.
So C alone can daily do = 12 – 3 – 4 = 5 units
So if C alone has to do the work, it will take him = 48/5 days

Question- 6 A can complete a piece of work in 18 days and B can do the same work in 15 days. After ten days, B left the work. In how many days can A alone finish the remaining work? (A) 5 days (B) 5.5 days (C) 6 days (D) 8 days

Explanation

Ans. (C)

Let total work done = LCM (18, 15) = 90
A can do this job in 18 days, so the daily work done by him will be 90/18 = 5 units.
B can do this job in 15 days, so the daily work done by him will be 90/15 = 6 units.
B worked for only 10 days. So in 10 days, he completed 106 = 60 units
The remaining work = 90 – 60 = 30 units
Thus, A will do the remaining work in = 30/5 = 6 days

Question- 7 A and B can do a piece of work in 5 days; B and C can do it in 7 days; A and C can do it in 4 days. In how much time can A, B and C together do the same work. (A) 280/83 days (B) 140/83 days (C) 70/83 days (D) None of these

Explanation

Ans. (A)

Let total work done = LCM (5, 7, 4) = 140
A and B can do a piece of work in 5 days so daily work done by A & B together = 140/5 = 28 units ——- (1)
B and C can do a piece of work in 7 days so daily work done by B & C together = 140/7 = 20 units ——— (2)
C and A can do a piece of work in 4 days so daily work done by C & A together = 140/4 = 35 units ——– (3)

So adding these 3 equations, we can say that
2A & 2B & 2C can together daily do = 28 + 20 + 35 = 83 units
or A, B & C can together daily do = 83/2 units
So A, B & C can together do the total work in =  = 280/83 days

Question- 8 A can finish a piece of work in 18 days and B can do the same in half the time taken by A. Then, working together, what part of the same work can they finish in a day? (A) 1/6 (B) 1/9 (C) 2/5 (D) None of these

Explanation

Ans. (A)

A can do this job in 18 days.
B takes half the time; it means he can do this job in 9 days.
Let total work done = LCM (18, 9) = 18
A can do this job in 18 days, so his daily work done will be 18/18 = 1 unit.
B can do this job in 9 days, so his daily work done will be 18/9 = 2 units.
So in a day, they can together do 1 + 2 = 3 units
Thus, the fraction of work done by them daily will be = 1/6

The efficacy of the approach described above has been claimed by students at the Institute for SSC CHSL Coaching in Delhi. In fact, even those enrolled in different Bank PO Coaching Classes have found it highly useful. However, it is only with consistent practice that you can master what has been discussed out here. So, it suggested that you solve around 80 to 100 questions on time and work. Doing so will give you a complete picture of the variations which can be introduced in this topic and you will be able to arrive at the correct answer, no matter how tricky the question may be.

Summary

The contents of this article will be instrumental in helping you score some assured marks in the exam. Make sure you have followed them well. However, if you have any confusion or require any kind of guidance, you can write to vidyagurudelhi@gmail.com and your queries will be answered by faculty members at Vidya Guru institute.