Time and Work is an important topic asked under the Arithmetic section in Mathematics. It is asked in various Defence Exams such as CDS, AFCAT, Air Force Group X & Y etc.
Today we are sharing with you some important questions asked under Time and work topic along with various approaches that you can follow to solve these questions.
We will continue this topic in various parts. We will discuss the basic questions that are usually asked in this topic and how you can solve them using the normal as well as Shortcut approach.
Important Tips & Tricks on Time & Work
A takes 8 days to finish a piece of work. B takes 10 days to finish the same work. How long will it take to finish the work when both of them are working together?
Now for such questions, A’s 1-day work = 1/8
B’s 1-day work = 1/10
Work done by both A and B together in one day = 1/8 + 1/10 = 9/40
Hence, A and B together will finish the work in 40/9 days.
While taking exam, you can express the information provided in the undermentioned form so that it consumes less time and space.
A takes 8 day to finish a piece of work. B takes 10 days to finish the same work. C takes 20 days to finish the work. How long will it take to finish the work when all are working together?
A takes 8 day to finish a piece of work. B takes 10 days to finish the same work. C takes 20 days to finish the work. D takes 40 days to finish the work. How long will it take to finish the work when all of them are working together?
B and C together can complete the work in 8 days. A and B together can complete the same work in 12 days while A and C together can complete it in 16 days.
(a) In how many days A, B and C together can complete the same work?
(b) In how many days A alone can complete the work?
(c) In how many days B alone can complete the work?
(d) In how many days C alone can complete the work?
If A+B can do a work in 10 days and A alone can complete the same work in 15 days. Find the no. of days taken by B to complete the work alone?
If A+B+C can do a work in 6 days, A+B can do a work in 8 days and A+C can do a work in 10 days.
Rohit can do a piece of work in 10 days, but with the help of Amit, he can do the same work in 6 days. In what time Amit can do the same work alone?
There are two gardeners A and B. Both plant some no. of trees in a garden in 10 days and 16 days respectively. In how many days both can complete the work together?
Now let’s discuss this same question by a different approach.
When time taken by A and B respectively is given, we can find the ratio of efficiency of A and B by taking inverse of their time.
Let’s do some examples to calculate efficiency.
If A and B alone do the same work in 14 and 18 days respectively, then ratio of efficiency of A and B.
Example 10 :
If A and B together complete the work in 10 days and B alone complete the same work in 15 days. In how many days can A alone complete the same work?
A is thrice as good as workman as B. Together they can finish a work in 12 days. In how many days will A finish the same work alone?
Use of Work Constant approach
While attempting questions, you must remember some important points -
1. Read the questions carefully.
2. Words like together, alone, before complete, after complete, etc. are important.
3. Data provided in the question should be read carefully.
How to approach and express data while taking the exam?
If there are two-person A and B. If A begins and both work alternate days. It means
Before going forward, we will discuss some basics of Ratios to make calculation easy for this topic and these basics will also help you in other topics like Partnership, time and distance, average, allegation etc.
TIME AND WORK EXAMPLES:
Example 5: A and B can do a work in 8 days and 12 days respectively.
Time (T) 8 days 12 days
Efficiency (η) 12 8
η 3 2
total work = TA× ηA = TB× ηB
total work = 8 × 3 = 12 × 2
total work = 24 units
(a). If both A and B work alternatively and A begins, then in how many days work will be completed?
According to question, A begins and both and b work alternately.
10th /2 day
Hence work will be completed in 9 (1/2) days.
But this type of approach is not helpful in exams. We will go by basic but in a smarter way.
If we make a pair of A and B, we can say that both together will work 5 units but in 2 days.
2 days = 5 unit of work
2 days × 4 = 5 units of work × 4
8 Days = 20 units of work, i.e. we can say that up to 8th day 20 units of work will be done
But on 9th day it’s a chance of A and he will do his 3 units of work. So till the 9th day, 23 units of work will be done. Now 1 unit of work will remain. On the 10th day, it’s a chance of B.
As above B do 2 unit of work in a day. So, he will do 1 unit of work in (1/2) days.
So total time taken to complete the work is 9 (1/2) days.
(b). If A and B both work for 4 days then A leaves. In how many days total work will be completed.
(EffA+B× tA+B )+( Eff.B × tB) = total work
(5 × 4)+(2 × tB) = 24
20 + 2 × tB = 24
2 × tB = 4
tB = 2 days , hence total time will be ( 4+2 )days i.e. 6 days.
Important: the Same question can be framed in many ways.
Way 1 : B works for 2 days and after that A joins B, then in how many days the work will be completed.
Solution: B works only for 2 days and then A joins B, i.e. both will work together after 2 days.
(tB × ηB) + (tA+B× ηA+B) = total work
(2 × 2) + (tA+B × 5) = 24
(tA+B × 5) = 20
tA+B = 4 days hence total time is (2+4) days i.e. 6 days
Way 2 : A and B both work together and A takes leaves for 2 days, then in how many days the work will be completed.
Solution: When both A and B are working together and A takes leaves for two days it means B has to work alone for 2 days .
Let total time to complete the work is t days.
So, ηA+B × (t-2) + ηB × 2 days = 24
5 × (t-2) + 2 × 2 = 24
t-2 = 4
t = 6 days Hence total time taken to complete the work is 6 days.
Don’t confuse between tA+B and TA+B (as mentioned in article1). Both are different.
Example 6: X can do a work in 6 days, Y can do it in 8 days and Z can do it in 12 days.
(a). If X starts the work and X, Y, Z works in alternate days, then in how many days the work will be completed?
Solution: Here X will start work on the 1st day, then Y will work on 2nd day and z will work on the 3rd day.
X : Y : Z
Time 6 : 8 : 12
Efficiency 12 × 8: 6 × 12 : 8 × 6
η 96 : 72 : 48
η 4 : 3 : 2
total work = ηX× TX= ηY×TY =ηZ×TZ
total work = 6 × 4 = 8 × 3 = 12 × 2 = 24 units
On 1st day, work done by X = 4 unit
On 2nd day, work done by Y = 3 unit
On 3rd day, work done by Z = 2 unit
Total work in 3 days done by X,Y and Z = 9 unit
Now again X will come then Y,then Z and so on till work is completed.
In 3 days = 9 units
× 2 × 2
In 6 days = 18 units
X will work on 7th day = 4 units
= 22 units
Now we need (24-22) units = 2 units work more but Y can do 3 unit of work in one day. So 2 unit will be done in (2/3) day.
+(2/3) day + 2 unit
Total days=7 (2/3) days 24 units
Hence total work will be done in 7 (2/3) days.
(b). If all started together and after completion of (3/4)th work, Y left and remaining work is done by X and Z together. Then in how many days work will be completed?
Solution: Total work is 24 units then (3/4)th work is 18 units.
One day work of (X+Y+Z) = 9 units so in 2 days 18 units of work will be done by (X+Y+Z) together.
After this Y left, X+Z worked together and 6 units of work remained.
One day work of X+Z = (4+2) units = 6 units. So in 3 days, total work will be completed.
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