LEVEL:

EASY

A can do a piece of work in 30 days. He works at it for 6 days and then B finishes it in 18 days. In what time can A and B together it ?
A) 14 (1/2) days B) 11 days
C) 13 (1/4) days D) 12 (6/7) days

Answer: D) 12 (6//7) days
Explanation:
Let 'B' alone can do the work in 'x' days
6/30 + 18/x = 1
=> x = 22.5
1/30 + 1/22.5 = 7/90
=> 90/7 = 12 (6/7) days

Twenty men can do a work in eighteen days. Eighteen women can complete the same work in fifteen days. What is the ratio between the capacity of a woman and a man ?
A) 4:5 B) 3:4
C) 4:3 D) 2:3

Answer: C) 4:3
Explanation:
(20 x 18) men can complete the work in in one day.
one man's one day work = 1/360
(18 x 15) women can complete the work in 1 day
1 woman's one day work = 1/270
So, required ratio = 1/270:1/360= 4:3

A can finish a work in 15 days and B can do the same work in 12 days . B worked for 8 days and left the job .In how many days, A alone can finish the remaining work?
A) 6 days B) 5 days
C) 4 days D) 3 days

Answer: B) 5 days
Explanation:
B's 8 days work=(1/12) x 8 = 2/3
Reaining work= 1/3
Now, 1/15 work is done by A in 1 day
Therefore, 1/3 work is done by A in 15 x (1/3) = 5 days

An air conditioner can coo the hall in 40 miutes while another takes 45 minutes to cool under similar conditions. If both air conditioners are switched on at same instance then how long will it take to cool the room approximately ?
A) 18 minutes B) 19 minutes
C) 22 minutes D) 24 minutes

Answer: C) 22 minutes
Explanation:
Let the two conditioners be A and B
'A' cools at 40min
'B' at 45min
Together =(axb)/(a+b) = (45x40)/85 = 21.1764 = (approx) 22 min.

When A, B and C are deployed for a task , A and B together do 70% of the work and B and C together do 50% of the work. who is most efficient?
A) A B) B C) C D) can't be determined

Answer: A) A
Explanation:
A + B= 70%
B + C =50%
[∵ (A+B)+(B+C)−(A+B+C)= B]
=> B= 20% A= 50% and C=30%
Hence A is most efficient

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) 1/24 days B) 7/24 days
C) 24/7 days D) 4 days

Answer: C) 24/7 days
Explanation:
(A+B+C)'s 1 day's work = (1/24 + 1/6 + 1/12) = 7/24
so, A,B and C together will complete the work in 24/7 days.

9 men and 12 boys finish a job in 12 days, 12 men and 12 boys finish it in 10 days. 10 men and 10 boys shall finish it in how many days ?
A) 15 days B) 11 days
C) 14 days D) 12 days

Answer: D) 12 days
Explanation:
9M + 12B  12 days ...........(1)
12M + 12B  10 days........(2)
10M + 10B ?
108M + 144B = 120M +120B
24B = 12M => 1M = 2B............(3)
From (1) & (3)
18B + 12B = 30B  12 days
20B + 10B = 30B ? => 12 days.

A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days ?
A) 9 days B) 11 days
C) 13 days D) 15 days

Answer: C) 13 days
Explanation:
Ratio of times taken by A and B = 100 : 130 = 10 : 13.
Suppose B takes x days to do the work.
Then, 10 : 13 :: 23 : x => x = ( 23 x 13/10 ) => x = 299 /10.
A's 1 day's work = 1/23 ;
B's 1 day's work = 10/299 .
(A + B)'s 1 day's work = ( 1/23 + 10/299 ) = 23/299 = 113 .
Therefore, A and B together can complete the work in 13 days.

4 men can repair a road in 7 hours. How many men are required to repair the road in 2 hours ?
A) 17 men B) 14 men
C) 13 men D) 16 men

Answer: B) 14 men
Explanation:
M x T / W = Constant
where, M= Men (no. of men)
T= Time taken
W= Work load
So, here we apply
M1 x T1/ W1 = M2 x T2 / W2
Given that, M1 = 4 men, T1 = 7 hours ; T2 = 2 hours, we have to find M2 =?
Note that here, W1 = W2 = 1 road, ie. equal work load.
Clearly, substituting in the above equation we get, M2 = 14 men

LEVEL

MEDIUM

A and B can do a work in 4 hours and 12 hours respectively. A starts the work at 6 AM and they work alternately for one hour each. When will the work be completed?
A) 4 days B) 5 days
C) 6 days D) 7 days

Answer: C) 6 days
Explanation:
Work donee by A and B in the first two hours, working alternatively = First hour A + Second hour B = (1/4) + (1/12) = 1/3.
Thus, the total time required to complete the work = 2 (3) = 6 days

A does half as much work as B and C does half as much work as A and B together. If C alone can finish the work in 40 days, then together ,all will finish the work in ?
A) 17 + 4/7 days B) 13 + 1/3 days
C) 15 + 3/2 days D) 16 days

Answer: B) 13 + 1/3 days
Explanation:
C alone can finish the work in 40 days.
As given C does half as much work as A and B together
=> (A + B) can do it in 20 days
(A + B)s 1 days wok = 1/20.
A's 1 days work : B's 1 days Work = 1/2 : 1 = 1:2(given)
A's 1 day’s work = (1/20) x (1/3) = (1/60) [Divide 1/20 in the raio 1:2]
B's 1 days work = (1/20) x (2/3) = 1/30
(A+B+C)'s 1 day's work = (1/60) + (1/30) + (1/40) = 9/120 = 3/40
All the three together will finish it in 40/3 = 13 and 1/3 days.

A and B can do a piece of work in 40 and 50 days. If they work at it an alternate days with A beginning in how many days, the work will be finished ?

(A+B)'s two days work = 1/40+1/50=9/200
Evidently, the work done by A and B duing 22 pairs of days
i.e in 44 days = 22×9/200=198/200
Remaining work = 1−198/200= 1/100
Now on 45th day A will have the turn to do 1/100 of the work and this work A will do in 40×1/100=25
Therefore, Total time taken = 44(2/5) days

6 boys and 8 girls can do job in 10 days , 26 boys & 48 women do work in 2 days. Find time taken by 15 boys and 20 girls to do same work ?
A) 2 days B) 3 days
C) 4 days D) 5 days

Answer: C) 4 days
Explanation:
One day work of 6 boys and 8 girls is given as 6b + 8g = 1/10 >(I)
One day work of 26 boys and 48 women is given as 26b + 48w = 1/2 >(II)
Divide both sides by 2 in (I) and then multiply both sides by 5
Now we get, 15b + 20g = 1/4.
Therefore, 15 boys and 20 girls can do the same work in 4 days.

12 men complete a work in 9 days. After they have worked for 6 days, 4 more men join them. How many days will they take to complete the remaining work ?
A) 2 days B) 2.5 days
C) 2.25 days D) 3 days

Answer: C) 2.25 days
Explanation:
1 man's 1 day work = 1/108
12 men's 6 day's work = 1/9 x 6 = 2/3
Remaining work = 1  2/3 = 1/3
16 men's 1 day work = 1/108 x 16 = 4/27
4/27 work is done by them in 1 day.
1/3 work is done by them in 27/4 x 1/3 = 9/4 days.

In a hostel, there was food for 1000 students for one month. After 10 days, 1000 more students joined the hostel. How long would the students be able to carry on with the remaining food?
A) 10 days B) 15 days
C) 20 days D) 5 days

Answer: A) 10 days
Explanation:
After 10 days, the remaining food would be sufficient for the 1000 students for 20 more days
>If 1000 more students are added, it shall be sufficient for only 10 days (as the no. of students is doubled, the days are halved).

Mr. stenley employed a certain number of typist for his project. 8 days later 20% of the typist left the job and it was found that it took as much time to complete the rest work from then as the entire work needed with all the employed typists. The average speed of a typist is 20 pages/hour. Minimum how many typist could be employed?
A) 10 B) 5
C) 15 D) 4

Answer: B) 5
Explanation:
Since 20% i.e 1/5 typists left the job. So, there can be any value which is multiple of 5 i.e, whose 20% is always an integer. Hence, 5 is the least possible value.

A tank has an inlet and outlet pipe. The inlet pipe fills the tank completely in 2 hours when the outlet pipe is plugged. The outlet pipe empties the tank completely in 6 hours when the inlet pipe is pluggeed.
If there is a lekage also which is capable of draining out the liquid from the tank at half of the rate of outet pipe,them what is the time taken to fill the emty tank when both the pipes are opened?
A) 3 hours B) 4 hours
C) 5 hours D) None of these

Answer: B) 4 hours
Explanation:
Rate of leakage = 8.33% per hour
Net efficiency = 50  (16.66 + 8.33)= 25%
Time required = 100/25 = 4 hours

P alone can complete a piece of work in 6 days. Work done by Q alone in one day is equal to onethird of the work done by P alone in one day. In how many days can the work be completed if P and Q work together ?
A) 5 (2/3) B) 6 (3/4 ) C) 4 (1/2) D) 3

Answer: C) 4 (1/2)
Explanation:
Work done by P alone in one day = 1/6th of the total work done by Q alone in one day = 1/3(of that done by P in one day) = 1/3(1/6 of the total) = 1/18 of the total.
Work done by P and Q, working together in one day = 1/6 + 1/18 = 4/18 = 2/9
They would take 9/2 days = 4 (1/2) days to complete the work working together.

Four pipes P,Q, R and S can fill a cistern in 20,25, 40 and 50 hours respectively.The first pipe P was opened at 6:00 am, Q at 8:00 am, R at 9:00 am and S at 10:00 am. when will the Cistern be full?
A) 4:18 pm B) 3:09 pm
C) 12:15 pm D) 11:09 am

Answer: B) 3:09 pm
Explanation:
Efficiency of P= 100/20= 5% per hour
Efficiency of Q= 100/25= 4% per hour
Efficiency of R= 100/40= 2.5% per hour
Efficiency of S=100/50= 2% per hour
Cistern filled till 10 am by P, Q and R
Till 10.00am Pipe P filled 20%
Till 10.00am Pipe Q filled 8%
Till 10.00am Pipe R filled 2.5%
TOTAL = 30.5%
Thus, at 10 am pipe P,Q and R filled 30.5% of the cistern.
Rest of cistern to be filled = 100  30.5 = 69.5%
Now, the time taken by P,Q,R and S together to fill the remaining capacity of the cistern
= 69.5 / (5+4+2.5+2) = 5 Hours and 9 minutes(approx).
Therefore, total time =4 hrs + 5hrs 9 mins = 9 hrs and 9 mins
It means cistern will be filled up at 3:09 pm

Kaushalya can do a work in 20 days, while kaikeyi can do the same work in 25 days. They started the work jointly.Few days later Sumitra also joined them and thus all of them completed the whole work in 10 days. All of them were paid total Rs.700. What is the Share of Sumitra?
A) Rs.130 B) Rs.185 C) Rs.70
D) can't be determined

Answer: C) Rs.70
Explanation:
Efficiency of kaushalya = 5%
Efficiency of kaikeyi = 4%
Thus, in 10 days working together they will complete only 90% of the work.
[(5+4)*10] =90
Hence, the remaining work will surely done by sumitra, which is 10%.
Thus, sumitra will get 10% of Rs. 700, which is Rs.70

LEVEL

DIFFICULT

A contractor undertakes to complete a work in 130 days. He employs 150 men for 25 days and they complete 1/4 of the work . He then reduces the number of men to 100, who work for 60 days, after which there are 10 days holidays.How many men must be employed for the remaining period to finish the work?

150 men in 25 days do = 1/4 work
Let 1 man in 1 day does = x work
Total work done by 150 men in 25 days = 150x * 25 = (1/4) work => x = (1/15000)
Therefore, 100 men in 60 days do = 100 * 60x = 6000x work = 6/15 = 2/5
Total work done =1/4 + 2/5 = 13/20
Therefore, Remaining work = (1  13/20) = 7/20
Remaining time = 130  (25+60+10) = 35 days
Therefore, work is done in 25 days by 150 men.
Therefore, Work is done in 35 days by 150 men.
Hence, he should employ 50 more men.

A is twice efficient as B and together they do the same work in as much time as C and D together. If C and D can complete the work in 20 and 30 daysrespectively, working alone ,then in how many days A can complete the work individually:
A) 12 days B) 18 days
C) 24 days D) 30 days

Answer: B) 18 days
Explanation:
A + B = C + D
   
Ratio of efficiency 10x + 5x 9x + 6x
________ _________
15x 15x
Therefore , ratio of efficiency of A:C =10:9
Therefore, ratio of days taken by A:C = 9:10
Therefore, number of days taken by A = 18 days

A contractor undertook a project to complete it in 20 days which needed 5 workers to work continuously for all the days estimated. But before the start of the work the client wanted to complete it earlier than the scheduled time, so the contractor calculated that he needed to increase 5 additional men every 2 days to complete the work in the time the client wanted it:
If the work was further increased by 50% but the contractor continues to increase the 5 workers o every 2 days then how many more days are required over the initial time specified by the client.
A) 1 day B) 2 days C) 5 days
D) None of these

Answer: B) 2 days
Explanation:
Total work = 100+50 = 150mandays
In 8 days 100 mandays work has been completed. Now on 9th and 10th day there will be 25 workers. So in 2 days they wll complete additional 50 man days work. Thus the work requires 2 more days.

3 men, 4 women and 6 children can complete a work in 7 days. A woman does double the work a man does and a child does half the work a man does. How many women alone can complete this work in 7 days ?
A) 6 B) 9
C) 5 D) 7

Answer: D) 7
Explanation:
Let 1 woman's 1 day work = x.
Then, 1 man's 1 day work = x/2 and 1 child's 1 day work x/4.
So, (3x/2 + 4x + + 6x/4) = 1/7
28x/4 = 1/7 => x = 1/49
1 woman alone can complete the work in 49 days.
So, to complete the work in 7 days, number of women required = 49/7 = 7.

A and B together can do a piece of work in 40 days. A having worked for 20 days, B finishes the remaining work alone in 60 days. In How many days shall B finish the whole work alone?
A) 60 B) 70
C) 80 D) 90

Answer: C) 80
Explanation:
Let A's 1 day's work=x and B's 1 day's work=y
Then x+y = 1/40 and 20x+60y=1
Solving these two equations , we get : x= 1/80 and y= 1/80
Therefore B's 1 day work = 1/80
Hence,B alone shall finish the whole work in 80 days

4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it ?
A) 40 days B) 36 days
C) 32 days D) 34 days

Answer: A) 40 days
Explanation:
Let 1 man's 1 day work = x and 1 woman's 1 day work = y.
Then, 4x + 6y = 1/8 and 3x + 7y = 1/10
Solving these two equations, we get:
x = 11/400 and y = 1/400
10 woman's 1 day work = (1/400 x 10) = 1/40.
Hence, 10 women will complete the work in 40 days

At Arihant Prakasham every book goes hrough 3 phases (or stages) typing, composing and binding. There are 16 typists, 10 composers and 15 binders. A typist can type 8 books in each hour, a composer can compose 12 books in each hour and a binder can bind 12 books in each hour. All of the people at Arihant Prakasham works for 10 hours a day and each person is trained to do only the ob of 1 category.How many books can be prepared in each day?
A) 1500 B) 1200
C) 1440 D) 1380

Answer: B) 1200
Explanation:
T C B
16 10 15
8 12 12
128 120 180
( in one hour<)
1280 1200 1800
in 10 hours <
Since, restriction is imposed by composers i.e,since only 1200 books can be composed i 10 hours so not more than 1200 books can be finally pepared.

A single reservoir supplies the petrol to the whole city, while the reservoir is fed by a single pipeline filling the reservoir with the stream of uniform volume. When the reservoir is full and if 40,000 liters of petrol is used daily, the suply fails in 90 days.If 32,000 liters of petrol is used daily, it fails in 60 days. How much petrol can be used daily with out the supply ever failing?
A) 64000 liters B) 56000 liters
C) 78000 liters D) 60000 liters

Answer: B) 56000 liters
Explanation:
Let x liter be the per day filling and v litr be the capacity of the reservoir, then
90x + v = 40000 * 90 (1)
60x + v= 32000 * 60 (2)
solving eq.(1) and (2) , we get
x = 56000
Hence , 56000 liters per day can be used without the failure of supply.

A contractor undertook to complete a piece of work in 120 Days and employed 140 men upon it. At the end of 66 days only half of the work was done,so he put on 25 extra men. By how much time did he exceed the specific time ?
A) 2 days B) 3 days
C) 4 days D) 5 days

Answer: A) 2 days
Explanation:
work done=total number of person x number of days;
half of work done = 140 x 66;
For half of remaining work 25 extra men are added.
Therefore, total men for half work remaining = 140 + 25 = 165;
Let 2nd half work will be completed in K days;
140 x 66 = 165 x K
K = 122;
Hence, extra days => 122120 = 2days.

There are three boats B1, B2 and B3 working together they carry 60 people in each trip. One day an early morning B1 carried 50 people in few trips alone. When it stopped carrying the passengers B2 and B3 started carrying the people together. It took a total of 10 trips to carry 300 people by B1, B2 and B3. It is known that each day on an average 300 people cross the river using only one of the 3 boats B1, B2 and B3. How many trips it would take to B1, to carry 150 passengers alone?
A) 15 B) 30
C) 25 D) 10

Answer: A) 15
Explanation:
Combined efficiency of all the three boats = 60 passenger/trip
Now, consider option(a)
15 trips and 150 passengers means efficiency of B1 = 10 passenger/trip
which means in carrying 50 passengers B1 must has taken 5 trips. So the rest trips equal to 5 (105 = 5) in which B2 and B3 together carried remaining 250 (300  50 = 250) Passengers.
Therefore the efficiency of B2 and B3 = 250/5 = 50 passenger/trip
Since, the combined efficiency of B1, B2 and B3 is 60. Which is same as given in the first statement hence option(a) is correct.

A take twice as much time as B or thrice as much time to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in ?
A) 3 hrs B) 6 hrs
C) 7 hrs D) 5 hrs

Answer: B) 6 hrs
Explanation:
Suppose A, B and C take x, x/2 and x/3 respectively to finish the work.
Then, (1/x + 2/x + 3/x) = 1/2
6/x = 1/2 => x = 12
So, B takes 6 hours to finish the work.

A can finish a work in 18 days and B can do the same work in half the time taken by A. then, working together, what part of the same work they can finish in a day ?
A) Total work B) Onefourth work
C) Half work D) Twothird work

Answer: C) Half work
Explanation:
A can do the work = 18 days
B can do the work = 18/2 = 9 days
(A + B)'s 1 day work = 1/18 + 1/9 = 1/6
=> In 3 days = 3x1/6 = 1/2 work is completed.

Two pipes A and B can fill a tank in 24 hours and 17(1/7) hours respectively. Harihar opened the pipes A and B to fill an empty tank and some times later he closed the taps A and B , when the tank was supposed to be full. After that it was found that the tank was emptied in 2.5 hours because an outlet pipe "C" connected to the tank was open from the beginning. If Harihar closed the pipe C instead of closing pipes A and B the remaining tank would have been filled in :
A) 2 hours B) 8 hours
C) 6 hours D) 4 hours

Answer: B) 8 hours
Explanation:
Efficiency of Inlet pipe A = 4.16% (100/24)
Efficiency of Inlet pipe B = 5.83% [100 divided17(1/7) ]
Therefore, Efficiency of A and B together = 100 %
Now, if the efficiency of outlet pipe be x% then in 10 hours the capacity of tank which will be filled = 10 * (10  x)
Now, since this amount of water is being emptied by 'C' at x% per hour, then
10x(10−x)x=2.5 hrs
=> x = 8
Therefore, in 10 hours 20% tank is filled only. Hence, the remaining 80% of the capacity will be filled by pipes A and B in 80/10 = 8 hours
