### Quantitative analysis Time and work aptitude test

INTRODUCTION:
The questions are based on the following factors.
The number of days taken by different persons
The efficiencies of different persons.
The work schedule.

SOME IMPORTANT POINTS:
(i) Number of days α 1/Efficiency.
(ii) Ratio between efficiency α 1/ Ratio of number of days.

METHOD :

Take the L.C.M of the number of days taken by different persons and consider it as the total part of the work.
By taking the L.C.M as the total part of the work, find out ,in 1 day they can do how many parts.
Then find out, the given work will be completed in how many number of days

QUESTIONs:
A can do a piece of work in 45 days & B in 40 days respectively. They worked together for some days & then A left the work & B completed the remaining work in 23 more days. After how many days, did A leave the work?
(a) 9 days.
(b) 10 days.
(c)11 days.
(d) 12 days.

QUESTION 1:
A can do a piece of work in 48 days & B in 96 days respectively. If they work together, the work will be completed in how many days?
(a) 30 days
(b) 32 days
(c) 33 days
(d)36 days

SOLUTION:
The total work is the L.C.M of 48 &96 i.e.96 parts.
In 1 day , A can do 2 parts & B 1part respectively.
Both can do 3 parts in 1day.
So, both can do 96 parts in 32 days.

QUESTION 2:
A can do a piece of work in 18 days, B in 24 days & C in 36 days respectively. If they work together , the work will be completed in how many days?
(a) 8 days
(b) 9 days
(c) 10 days
(d)12 days

SOLUTION:
The total part of the work is the L.C.M of 18,24 &36 i.e. 72 parts.
In 1 day A can do 4 parts ,B 3 parts & C 2 parts respectively.
So all together they can complete 9 parts in 1 day & total 72 parts in 8 days.

QUESTION 3:
A& B can do a piece of work in 20 days, B & C in 30 days and C & A in 40 days respectively. If they work together, the work will be completed in how many days?
(a) 17 6/13 days.
(b) 18 6/13 days.
(c) 18 ½ days.
(d) 19 days.

SOLUTION:
The total work is the L.C.M of 20,30 & 40 i.e. 120 part.
In 1 day A & B can do 6 parts &C can do 4 parts and C & A can do 3 parts respectively.
When 2 ( A + B+ C) work , they can do 6 + 4+3 i.e.13 parts in 1 day.
So, A +B +C can do 6.5 parts in 1 day & 120 parts in …
18 6/13 days.

QUESTION 4:
In the above question, If they work separately, the work will be completed in how many days?
(a) 48,34 2/7,240 days.
(b) 36,48,72 days.
(c) 48,72,120 days.
(d) 72,120,240 days.

SOLUTION:
A +B+C can do 6.5 parts in 1 day.
A+B can do 6 parts, B+C can do 4 parts C+A can do 3 parts.
So A can do 6.5-4=2.5 parts in 1 day & 120 parts in 48 days.
B can do6.5-3=3.5 parts in 1 day & 120 parts in 34 2/7 days.
Similarly, C can do 6.5-6 =.5 part in 1 day & 120 parts in 240 days.

QUESTION 5:
A can do a piece of work in 12 days & B in 15 days and they work on alternate days. The work will be completed in how many days:
(i) If A starts the work?
(ii) If B start the work?
(a) 13 ¼ & 13 2/5 days.
(b) 13 ¼ &13 ½ days.
(c) 12 & 13 days.
(d) !2 ½ &13 ½ days.

SOLUTION:
The total work is the L.C.M of 12 & 15 i.e.60 parts.
In1 day A can do 5 parts & B 4 parts.
So they can do 9 parts in 2 days.
And 54 parts in 12 days.
Then (i) if A starts, he can complete 5 parts out of the rest 6 parts in 1 day & then B can complete the rest 1 part in ¼ day.
So the work will be completed in 12 +1+1/4 i.e.13 ¼ days.
(ii) If B starts, He can complete 4 parts out of rest 6 parts in 1 day & then A can complete the rest 2 parts in 2/5 days.
So the work will be completed in 12+1+2/5 i.e.13 2/5 days.

SOLUTION:
The total work is the L.C.M of 45 & 40 i.e. 360 parts.
In 1 day A can do 8 parts & B 9 parts respectively.
In the last 23 days B can complete 23*( i.e. 207 parts.
So the rest work must have been completed by them.
A & B can do 8 +9 i.e.17 parts in 1 day.
So they have done 153 parts in 9 days and then A left the work.

QUESTION 7:
A &B can do a piece of work in 12 days, B&C in 16 days respectively. After A has been working for 5 days and B for 7 days, C takes up and finishes it alone in 13 days. In how many days they can do it separately/
(a) 12,16,18 days.
(b) 16,48 & 24 days.
(c) 16, 18& 24 days.
(d) 24,36 & 48 days.

SOLUTION:
The total work is the L.C.M of 12 &16 i.e.48 parts.
In 1 day A & B can do 5 parts and B & C can do 3 parts.
According to question, 5 days work of A + 7 days work of B + 13 days work of C is the total work.
We can not take their individual work , so we can convert the above work as 5 days work of A & B + 2 days work of B & C + 11 days work of C .
In 5 days A & B can do 20 parts ,In 2 days B & C can do 6 parts . So C can do the rest 22 parts in 11 days.
From the above C can do 2 parts in 1 day & 48 parts in 24 days.
And B can do 3-2 i.e. 1 part in 1 day & 48 parts in 48 days.
Similarly A can do 4-1 i.e.3 parts in 1 day & 48 parts in 16 days.

QUESTION 8:
If 2 men or 3 women or 4 boys can do a piece of work in 49 days, then 3 men,4 women & 5 boys can do it in how many days?
(a) 10 days.
(b) 12 days.
(c) 15 days.
(d) 18 days.

SOLUTION:
Take the product of the number of men,women,boys & number of days as the total part of the work i.e.2*3*4*49.
Then 3 men can do 3*3*4 i.e. 36 parts,4 women 4*2*4 i.e.32 parts & 5 boys can do 5*2*3 i.e.30 parts in 1 day.
So 3 men, 4 women % boys can do 98 parts in 1 day & 2*3*4*49 parts in 12 days.

QUESTION 9:
A is thrice as fast as B, and is there fore able to do a work in 60 days less than B. If they work together, the work will be completed in how many days?
(a) 20 days.
(b) 22.5 days.
(c)24 days.
(d) 25 days.

SOLUTION:
The ratio between efficiency between A & B is 3:1.
So the ratio between number of days taken by A & B is 1:3.(As number of days α1/efficiency)
A takes 2 parts less days than B i.e.60 days.
So 1 part days i.e.30 which A takes &3 parts days i.e.90 which B takes.
The total work is the L.C.M of30 & 90 i.e.90parts.
A & B can do 4 parts in 1 day, So total work 90 parts in 22.5 days.

QUESTION 10:
A is twice as a good work man as B & together can complete a piece of work in 21 days. If they work separately, the work will be completed in how many days?
(a)31.5 & 63 days.
(b) 32 & 63 days.
(c)21 & 63 days.
(d) None of these.

SOLUTION:
If the efficiency of B is 1 part, the efficiency of A is 2 parts.
So, in 1 day both can do3 parts & in 21 days the total work 63 parts.
A can do 2 parts in 1 day, so 63 parts in 31.5 days.
B can do 1 part in 1 day, so 63 parts in 63 days.

QUESTION 11:
A builder decided to build a farmhouse in 40 days. He employed 100 men in the beginning and 100 more after 35 days and completed the construction in stipulated time. If he had not employed the additional men, how many days behind the schedule would it have been finished?
(a) 3 days.
(b) 4 days.
(c) 5 days.
(d) 6 days.

SOLUTION:
The contractor has employed 100 men for 35 days and 200 men for the last 5 days.
The working capacity of 200 men in 5 days=The working capacity of 100 men in 10 days.
So if he had not employed another 100 men, the work would have been completed 5 days behind the schedule

QUESTION 12:
A,B and C can do a work in 8,16 and 24 days respectively. They all begin together, A continues to work till it is finished, C leaving off 2 days and B one day before its completion. In what time is the work finished?
(a) 5 days.
(b) 6 days.
(c)8 days.
(d) 9 days.

SOLUTION:
The total work is the L.C.M of 8,16,24 i.e.48 parts.
In1 day, A can do6 parts, B 3 parts & C 2 parts.
The working schedule is as follows:
(A,B & C )’s work for same days +(A &B)’ s work for 1 day + A’s work for 1 day.
So in the last 2 days , the extra work done by A+B & A is 9+6=15 parts.
That means all have done the rest part i.e. 33 parts.
A,B & C can do 11 parts in 1 day, So they have done 33 parts in 3 days.
So the total number of days=3+2=5 days.

QUESTION 13:
There is sufficient food for 400 men for 31 days. After 28 days 280 men leave the place. For how many days will the rest food last for the rest of the men?
(a) 8 days.
(b) 10 days.
(c)12 days.
(d) 15 days.

SOLUTION:
After 28 days ,the rest food is sufficient for400 men for the next 3 days.
If 280 men leave, then the rest food is sufficient for the rest 120 men for 10 days.

QUESTION 14:
A contractor under took to build a road of 15 km in 12 days. He employed 100 men in the beginning and after 6 days, he observed that only 6 km of road has been completed. In order to complete the work in the stipulated time, how many extra men are needed?
(a) 50.
(b) 75.
(c)100.
(d) None of these.

SOLUTION:
After 6 days, the rest work of 9 km has to be completed in the last 6 days.
If 100 men can complete 6 km in 6 days, then they can complete 9 km in9 days.
But, the rest work of 9 km has to be completed in 6 days by 150 men.
So, the extra number of men are:
150-100=50.

QUESTION 15:
A and B working together can finish a job in T days. If A works alone and completes the job, he will take T + 5 days. If B works alone and completes the same job, he will take T + 45 days. What is T?

A.25
nB.60
nC.15
nD .None of these

SOLUTION

A+B can finish a job in T days
A works alone to finish the job in T+5 days.
Similarly B takes to finish the job in T+45 days.
In 1 day A+B will finish 1/T parts of the work. And A will finish 1/(T+5) parts B will finish 1/(T+45) parts.
Therefore
1/T = 1/(T+5) + 1/(T+45)
Solving the above equation we get
=> T2 =225 , => T = (225)1/2
Therefore T = 15

QUESTION16:
A certain number of men can do a piece of work in 45 days. If there were 12 men less it could be completed in 15 days more. How many men were originally there.
A.36 men.
B.40 men.
C.44 men.
D.48 men.

SOLUTION
The ratio between the number of days taken by original number of men and new men is 45:60 i.e.3:4.
So the ratio between the number of persons is 4:3.(As number of days α1/number of persons.)
Due to 12 men less, the number of person decreases by 1 parts.
So 1 part =12 men
And original number of men is 4 parts i.e.48.

QUESTION 17:
A, B and C can do a work in 5 days, 10 days and 15 days respectively. They started together to do the work but after 2 days A and B left. C did the remaining work (in days) ?

A.1
nB.2
nC.3
nD.4

SOLUTION:
Total work i.e. L.C.M of 5,10,15 = 30 parts
In 1 day A can do 6 parts, B can do 3 parts, C can do 2 parts of the work,
In 1 day (A+B+C) can do (6+3+2) = 11 parts
In 2 days (A+B+C) can do 22 parts
The rest part of the work = (30-22)=8 parts
C can do 2 parts in 1 day => C can do 8 parts in 4 days.

QUESTION 18:
X alone can do a piece of work in 15 days and Y alone can do it in 10 days. X and Y undertook to do it for Rs.720. With the help of Z they finished it in 5 days. How much is paid to Z?

–Rs.360
–Rs.120
–Rs.240
–Rs.300

SOLUTION:
The total part of work is L.C.M of 15,10,5 = 30
In 1 day X can do 2 parts, Y can do 3 parts, (X+Y+Z) can do 6 parts.
Z can do 6-(2+3) = 1 part in 1 day.
Ratio of efficiency between X, Y and Z is 2:3:1
According to the ratio of 2:3:1 the total wage Rs270 will be divided among them
Total 6 parts = Rs720
So Share of Z i.e. 1 part = Rs120

QUESTION 19:
Ram starts working on a job and works on it for 12 days and completes 40% of the work. To help him complete the work, he employs Ravi and together they work for another 12 days and the work gets completed. How much more efficient is Ram than Ravi?
A.50%.
B.60%.
C.100%.
D.125%.

SOLUTION:

Ram can do 40% of the work in 12 days
Ram can do 100% of the work in (12/40) * 100 = 30 days
Ram + Ravi can do 60% of the work in 12 days
Ram + Ravi can do 100% of the work in 20 days
L.C.M of 20 and 30 = 60, So total work = 60 parts
In 1 day Ram + Ravi can do 3 parts of the work while Ram can do 2 parts
Ram can do 1 part of the work in 1 day
And So Ram is 100% more efficient than Ravi

QUESTION 20:

A red light flashes 3 times per minute and a green light flashes 5 times in two minutes at regular intervals. If both lights start flashing at the same time, how many times do they flash together in each hour?
A.20.
B.24.
C.30.
D.32.

SOLUTION:

A red light flashes 3 times per minute
A green light flashes 5 times in two minutes
In 1 hr red light flashes 180 times and green light 150 times
In 1 hr both flash for the H.C.F of (150,180) = 30 times.

QUESTION 21:

A and B can do a piece of work in 21 and 24 days respectively. They started the work together and after some days A leaves the work and B completes the remaining work in 9 days. After how many days did A leave?

–5
–7
–8
–6

SOLUTION:

Total work i.e. L.C.M of 21 and 24 = 168 parts
A can do 8 parts and B can do 7 parts in 1 day
B has done some part of the work alone i.e. 7*9= 63 parts in the last 9 days.
Before the 63 parts , they both have done (168-63) parts= 105 parts
A and B can do 15 parts of work i.e. (8+7) parts in 1 day
Therefore A+B can do 105 parts in (105/15)= 7 days.

QUESTION 22:
Ram, who is half as efficient as Krish, will take 24 days to complete a work if he worked alone. If Ram and Krish worked together, how long will they take to complete the work?

–16 days
–12 days
–8 days
–18 days

SOLUTION:

The ratio between the efficiency of Ram and Krish = 1:2
By working 1 part in 1 day Ram completed the work in 24 days
By working 3 parts in 1 day Ram and Krish can complete the work in
24/3= 8 days.

QUESTION 23:
A can do a piece of work in 20 days in 30 days & C in 40 days respectively. If they work on alternate days & A starts the work, the work will be completed in how many days?
A.27 days.
B.27 ½ days.
C.28 days.
D.30 days.

SOLUTION:
The total work is the L.C.M. of 20,30,40 i.e.120 parts.
So, in I day A can do 6 parts, B 4 parts & C 3 parts.
If they work on alternate days, they can do 13 parts in 3 days.
So ,they can do 117 parts in 27 days.
If A starts, after 27 days he will complete the rest parts i.e.120-117=3 parts in ½ days.
So, the work will be completed in 27 ½ days.

QUESTION 24:
A can do a piece of work in 18 days, B in 24 days & C in 36 days respectively. If they work together the work will be completed in how many numbers of days?
A.8 days
B.9 days.
C.10 days.
D.12 days.

SOLUTION:

Total part of the work is the L.C.M of 18, 24, 36 i.e. 72 & in 1 day A can do 4 parts, B can do 3 parts & C can do 2 parts respectively.
So, altogether A, B, C can do 9 parts in 1 day.
That’s why they can do total work 72 parts in 8 days.

QUESTION 25:
A & B can do a piece of work in 20 days, B & C in 30 days & C& A in 40 days respectively. If they work together, the work will be completed in how many numbers of days?
A.18 days.
B.18 ½ days.
C.18 6/13 days.
D.18 7/13 days.

SOLUTION:
Total part of the work is the L.C.M of 20,30 & 40 is 120.
So in 1 day A & B can do 6 parts, B & C can do 4 parts, C and A can do 3 parts respectively.
When all these persons work together i.e., 2(A+B+C) they can do 13 parts in 1day.
So (A+B+C) they can do 6.5 parts in 1 day &120 parts in 18 6/13 days .

QUESTION 26:

If A & B can do a piece of work in 10 days & A can do it in 30 days, then B can do it in how many days?
A.12 days.
B.15 days.
C.18 days.
D.20 days.

SOLUTION:

Total part of the work is the L.C.M of 10 & 30 i.e. 30 parts.
So in 1 day A & B can do 3 parts & A can do 1 part respectively.
There fore B can do 2 parts in 1 day
That’s why B can do 30 parts in 15 days

QUESTION 27:
A certain number of men can do a piece of work in 45 days. But if there were 10 men less, it could be completed in 15 days more. How many men were there originally?
A.36
B.40
C.48
D.50

SOLUTION:
The number of days taken by the original number of men is 45 & due to 10 men less it is 60 days.
That means the ratio between the numbers of days is 3: 4.
So that the ratio between the numbers of persons is just reverse of it i.e. 4:3 (As number of days & number of persons are inversely proportional to each other)
In this case there is a decrease of 1 part in number of persons due to 10 men less. So the number of men originally which is 4 parts i.e. 40.

QUESTION 28:

If 3 men or 4 boys can do a piece of work in 19 days, then 5 men & 6 women can do it in how many days?
A.5 days.
B.6 days.
C.8 days.
D.9 days.

SOLUTION:
The total part of the work is the L.C.M of the no of men, boys & days from the first case i.e. 3 *4*19 parts. (Don’t multiply them just keep like this.)
In 1 day 5 men can do 5*4 = 20 parts (which is the product of this 5 men with the number of boys from the first case ) & 6 boys can do 6*3=18 parts (which is the product of this 6 boys with the number of men from the first case) .
So that 5 men & 6 boys can do 20+18=38 parts in 1 day. There fore they can do 3 *4*19 parts in 6 days.

QUESTION 29:
To do a piece of work, B takes 3 times as long as A & C together, and C twice as long as A & B together. If the three together can complete the work in 10 days, how long would A take by him self?
A.20 days.
B.24 days.
C.25 days.
D.30 days.

SOLUTION:
3 times B's daily work=(A+C) 's daily work.
So 4 times of B's daily work = (A+B+C) 's daily work. That’s why if (A+B+C) can do a piece of work in 10 days, then B can do it in 40 days.
Similarly , 2 times C's daily work =(A+B) 's daily work
=> 3 times C’s daily work = (A+B+C) 's daily work .
=> C can do the work in 30 days
From the above (A+B+C) can do the work in 10 days , B can do it in 40 days & C can do it in 30 days.
=> Total parts of the work is the L.C.M of 10, 40, 30 i.e. 120 parts. So (A+B+C) can do 12 parts, B can do 3 parts & C can do 4 parts in 14 day.
=> A can do 5 parts in 1 day. So A can do the whole work i.e. 120 parts in 24 days

QUESTION 30:
10 men can finish a piece of work in 10 days, where as it takes 12 women to finish it in 10 days. If 15 men and 6 women undertake to complete the work, how many days will they take to complete it?
A.4 days.
B. 5 days.
C. 6 days.
D. 9 days

SOLUTION:
The working capacity of 10 men=12 women.
Take the product of the number of men, women& days from the first case & consider it as the total part of the work.
So, the total work is 10*12*10 parts.
In this case,15 men can do15*12i.e.180 parts & 6 women can do6*10 i.e.60 parts in 1 day.
So, they can do 10*12*10 parts in 5 days.

QUESTION 31:
3 men and 4 boys do a piece of work in 8 days, while 4 men and 4 boys do the same work in 6 days. In how many days will 2 men and 4 boys finish the work?
A.10 days.
B.12 days.
C.15 days.
D.24 days.

SOLUTION:
If the L.C.M of 8 & 6 i.e.. the total part of the work is 24 parts.
In 1 day,3 men & 4 boys can do 3 parts & 4 men and 4 boys can do 4 parts.
So, 1 man can do 1 part in and 1 boy can do nothing in 1 day.
That’s why 2 men & 4 boys can do 24 parts in 12 days.

QUESTION 32:
A can do a work in 30 days and B can do the same work in 40 days. They work together for 5 days and then B goes away. In how many days will A finish the remaining work?
A.21 ¼ days.
B.21 ½ days.
C.21 1/3 days
D.24 days.

SOLUTION:
The total work is the L.C.M of 30 & 40 i.e.120 parts.
In 1 day A can do 4 parts & B 3 parts.
In 1 day, both can do 7 parts & in 5 days 35 parts.
When B goes away, the rest part of work is 85 parts.
A can do 4 parts in 1 day, so 85 parts in 21 ¼ days.

QUESTION 33:
A takes as much time as B & C together take to finish the job. A & B working together finish the job in 10 days. C alone can do the same job in 15 days. In how many days can B alone do the same work?
A.40 days
B.50 days.
C.60 days.
D.80 days.

QUESTION 34:
A started a work and left after working for 2 days. Then B was called and he finished the work in 9 days. Had A left the work after working for 3 days, B would have finished in 6 days. In how many days can each of them, working alone, finish the whole work?
A.6 & 12 days.
B.5 & 15 days.
C.6 & 18 days.
D.5 & 12 days.

QUESTION 35:
One man, 3 women and 4 boys can do a work in 96 hours; 2 men and 8 boys can do it in 80 hours; and 2 men and 3 women can do it in 120 hours. In how many hours can it be done by 5 men and 12 boys?
A.42 hours
B.43 ½ hours.
C.43 7/11 hours.
D.45 hours.

SOLUTION:
1 man +3 women + 4 boys can do a work in 96 hrs,so 2 men + 6 women+8 boys can do the work in 48 hrs.
Again, 2 men +8 boys can do the work in 80 hrs.
And also,2 men+4 women can do the work in 120 hrs.
So if we take the L.C.M of 48, 80 & 120 i.e.240 parts as the total work, then 2 men+6 women+8 boys can do 5 parts,2 men+8 boys 3 parts & 2 men+4 women 2 parts in 1 hr.
From the above 1 man can do 1/3 parts & 1 woman can do1/3 part & 1 boy can do 7/24 parts in 1 day.
So 5 men & 12 boys can do……..