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A can do a piece of work in 12 days and B in 15 days. Find how much time they will take to complete the 
work under the following conditions.

1. Working alternately starting with A 

Work starting with A
So Work done in 2 day = 1/12+1/15 = 9/60
total work done in 12 day = 54/60
remain work =1/10
work done by A on 13th day .
after 13day  remain = 1/60
on 14th day  B have to work 1/4 th time of day.

2. Working alternately starting with B

Same way if starting with B .on 14 day work will done by A around 2/5 th (approx)time  of day .
.

3. When both of them are working together and B leaves 2 days before the actual completion of work, 
then find the total time required to complete the job.

in last 2 day work done by Aso remain work = 60-10 = 50
So total required day = 50/9+2 = 7.5 (approx)

4. If another person C who does negative work, work against A and B and can completely destroy the
 work in 25 days, joins them and they work together all the time. How much time required completing the
 work?

C does negative work .So total days to complete the work =1 /( 1/12+1/15-1/25 ) = approx 9.09 days

5. A sum of Rs. 6600 was taken as a loan. This is to be repaid in two equal annual installments. If the 
of interest be 20% compounded annually then the value of each installment is

A) 4320

B) 4400

C) 4500

D) 4220

E) None of these .
interest is compounded annually .
and we have to give equal installment.
let each installment is x rs.
x/(1+20/100) + x/(1+20/100)^2 = 6600
on solving x = 4320.

Directions (6-10) Study the following graph carefully and answer the questions given below India's Export
 of rice over the years (in lakh tonnes)

6. What was the percentage increase in export of rice from 1991 to 1992?

18*100/15

 20

7. The total export of rice in 1994 was what percent of the total export in the year 1991 and 1993?

 20*100/40
 50 

8. What was the percentage drop in the export of rice in the year 1994 as compared to the year 1993?

 20*100/25=80 So 20% Drop out
 20

9. In how many years the export of rice were less than the average export in the given year s?

 Average = 22
,In Graph We saw Below 22 (1991,1992,1994)
 3  

10.In which of the following pair of years the difference in export is maximum?

 1991-1995 

11. A can do a work in 50 days and B in 40 days . They work together for 10 days and then A leaves and  B

Let the total work be 200 work
Efficiency of
A = 200/50 = 4 work/day
B = 200/40 = 5 work/day
A+B’s efficiency = 9/day
A+B’s 10 days work = 9*10 = 90
Remaining work = 200-90 = 110
Time taken by B alone to finish the remaining wrk = 110/5 = 22days

22. 30 men, working 4 hrs a day can do a piece of work in 10 days. Find the number of days in which 45 men
 working 8 hrs a day can do twice the work. Assume that 2 men of the first group do as much work in 2 hrs
 as 4 men of the second group do in 1 hr.
6(2/3) days
Efficiency of first group : 2nd group = 2*2 :4*1 = 1:1

D2 = 30*4*10*1*2 / 45*8*1*1
D2 = 20/3 = 6(2/3) days

23. A alone would take 27 hrs more to complete the job than if both A and B would together. If B worked 
, he took 3 hrs more to complete the job than A and B worked together. What time, would they take if both
 A and B worked together?

 9 HoursLet A+B together takes X hours
A will take X+27 hrs
B will take X+3 hrs
Let the total work be (X+27)(X+3)
Efficiency of A= X+3
B = X+27
Total efficiency = 2X+30
Time working together = (X+27)(X+3) / 2X+30 = X
 X^2 +30X + 81 = 2X^2 + 30X
or, X^2 = 81 or X= 9 hrs (neglecting –Ve time )

24. A and B together can do a piece of work in 12 days which B and C together will do in 16 days. After A 
has been working on it for 5 days, and B for 7 days, C finishes it in 13 days. In how many days A,B and C 
alone will do the work ?

 (b) 16, 48 and 24 days respectivelyLet the total work be 48
Efficiency of
A+B = 4/day…… (i)
B+C = 3/day……..(ii)
Now, A works for 5 days, B works for 7 days and C works for 13 days and completes the total work of 48.
This can be rewritten as
A+B for 5 days + B+C for 2 days + C for 11 days completes the total work of 48
Now, A+B’s 5 days work = 20
B+C’s 2 days work = 6
Therefore, 20+6+ C’s 11 days work = 48
C’s  11 days work = 48-26 = 22
C’s efficiency = 2/day.. (iii)
From (i),(ii),(iii)
C’s efficiency = 2
B’s Efficiency = 1
A’s efficiency = 3
Time taken by
A= 16 days, B= 48 days, and C= 24 days

25. Two women Ganga and Jamuna, working separately can mow a field in 8 and 12 hours respectively. If 
they work for an hour alternately, Ganga beginning at 9 am, when will the mowing be finished?

(e) None of these (6:30PM)Let the total work be 24
Efficiency of Ganga = 24/8 = 3/hr
Efficiency of Jamuna= 24/12 = 2/hr
They work alternately starting from Ganga
First 2 hrs work = 3+2 = 5
First 8 hrs work = 20
Remaining = 24-20 = 4
9th hr work to be done by Ganga = 3
Remaining work = 4-3 = 1 to be done by Jamuna in 1/2 hr.
Total time = 8+1+(1/2) hrs = 9.5 hrs or 9 Hr 30 minutes
So work will be completed by 9AM + 9 hrs 30 minutes = 18 hrs 30 minutes or 6:30 PM

26. A, B and C together can do a work in 12 days. A alone can do the work in 36 days and B alone can do
 the same work in 54 days. Find in what time C alone can do that work?

(d) 27 DaysLet the total work be 108 (Common Multiple of 12,36 and 54)
Efficiency of A+B+C =108/12=  9,
of A alone = 108/36 = 3 and
of B alone = 108/54 = 2
Therefore of C alone = 9-(3+2) = 4
Time taken by C = 108/4 = 27 days

27. A, B and C together can do a work in 4 days. A alone can do the work in 12 days B alone can do the 
same work in 18 days. Find in what time C alone can do the same work alone?

(a) 9 DaysLet the total work be 36 ( Can take any value Preferably Common Multiple )
Efficiency of
A+B+C = 36/4 = 9
A alone= 36/12 = 3
B alone = 36/18 = 2
C alone = A+B+C- (A+B) = 9-(3+2) = 4
Time taken by C alone = 36/4 = 9 days

28. A can complete a work in 35 days and B can do the same work in 28 days. If A after doing 10 days,
 leaves the work , find in how many days B will do the remaining work?

None of these (20 days)Let the total work be 140
Efficiency of A = 4
Efficiency of B = 5
A works for 10 days = 4*10 = 40
Remaining work = 140-40 = 100 to be done by B
B will do it in 100/5 = 20 days

29. A can complete a work in 24 days and B can complete the same work in 18 days. If A after doing 4 days 
leaves the work find in how many days B will complete the remaining work?

15 daysLet the total work be 72
Efficiency of A = 3 and Of B = 4
A’s 4 days work = 3*4 = 12 remaining work = 72 -12 = 60
Work completed by B in 60/4 = 15 days

30. A and B together can do a piece of work in 6 days, B alone could do it in 8 days. Supposing B works at
 it for 5 days, in how many days A alone could finish the remaining work?

9 daysLet the total work be 24
Efficiency of A+B = 4
Efficiency of B = 3
Efficiency of A = 1 as A+B = 4 and B= 3
Work done by B in 5 day = 3*5 = 15
Remaining work = 24-15 = 9
Remaining work to be done by A in 9/1 = 9 day

31. A and B can do a piece of work in 20 days and 30 days. both starts the work together for some time,
but B leaves the job 5 days before the work is completed. Find the time in which work is completed.

(c) 14 daysLet the total work be 60
Efficiency of A = 3 and of B = 2
Efficiency of A+B = 3+2 = 5
Suppose B never left the work then if the time taken remains same then work done by B in those 5 days will be
 added to original work.
Therefore, Now, works become = 60 + B’s 5 days work = 60+10 = 70
Time taken = 70/5 = 14 days

32. Two pipes A & B can fill a tank in 36 hours and 45 hours respectively. If both the pipes are open 
simultaneously. How much times will be taken to fill the tank?

Required Time = 1/(1/45+1/36)= 20 hour

33. If A & B two pipes can fill a tank in 10 hour, when A pipe can fill a tank in 6 hour alone ,then in how 
much time will be taken to fill/empty the tank when pipe B open alone ?

1/6+ 1/B= 1/10So B = -60/4 =-15
So b will empty the tank in 15 hour

34. Pipe A and B can fill a tank in 10 hour and 12 hour respectively but pipe C can empty the same tank in
 15 hour, In how much time it will take fill the tank when the three pipes are opened together? 

Total Time = 1/(1/10 + 1/12-1/15)= 8.5 hour

35. Two pipes A & B fill an empty tank in 40 minutes and 60 minutes respectively, If both pipes are open
 simultaneously after how much time should A be closed so that tank is filled in 36 minutes? 

Pipe B will work for 36 min.in 36 min he will fill the part of tank = 36/60 =3/5 part
Remain part = 2/5
it will filled by A in minutes = 2/5*40 = 16 min
So Tap A should be closed after 16 minutes to fill the tank in 36 minutes.