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__Time And Work__
1. A can do a work in 50 days and B in 40 days .
They work together for 10 days. and then A leaves B to finish the work alone.
How long will B take to finish it??

(a) 11 days

(b) 18 days

(c) 22 days

(d) 26 days

(e) None of these

2. 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 wrk in 2
hrs as 4 men of the second group do in 1 hr.

(a) 6(1/3) days

(b) 6(2/3) days

(c) 5(3/6) days

(d) 3(1/6) days

(e) None of these

3. A alone would take 27 hrs more to complete the
job than if both A and B would together. If B worked alone, 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?

(a) 8 hours

(b) 10 hours

(c) 9 hours

(d) 6 hours

(e) None of these

4. 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 ?

(a) 16, 48 and 26
days respectively

(b) 16, 48 and 24
days respectively

(c) 26, 48 and 24
days respectively

(d) 16, 46 and 24
days respectively

(e) None of these

5. 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?

(a) 9:30 PM

(b) 8:30 PM

(c) 6:00 AM

(d) 7:00 PM

(e) None of these

6. 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?

(a) 9 days

(b) 18 days

(c) 24 days

(d) 27 days

(e) None of these

7. 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 days

(b) 18 days

(c) 27 days

(d) 8 days

(e) None of these

8. 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?

(a) 15 days

(b) 10 days

(c) 27 days

(d) 24 days

(e) None of these

9. 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?

(a) 11 days

(b) 15 days

(c) 12 days

(d) 10 days

(e) None of these

10. 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?

(a) 9 days

(b) 8 days

(c) 24 days

(d) 12 days

(e) None of these

11. 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.

(a) 7 days

(b) 12 days

(c) 14 days

(d) 16 days

(e) None of these

__Answers :-__**1. (c) 22 days**

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

**2. 6(2/3) days**

<i> Solution:- M1D1H1E1W2 = M2D2H2E2W1 (From
MDH Rule)

Efficinecy of first grp : 2nd grp = 2*2 :4*1 = 1:1

Now, D2 = M1D1H1E1W2 / M2H2E2W1

D2 = 30*4*10*1*2 / 45*8*1*1

D2 = 20/3 = 6(2/3) days

**3. (c) 9 Hours**

Let 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 )

**4.**

**(b) 16, 48 and 24 days respectively**

Let 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

**5. (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

**6. (d) 27 Days**

Let 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

**7. (a) 9 Days**

Let 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

**8. (e) 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

**9. (b) 15 days**

Let 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

**10. (a) 9 days**

Let 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 days

**11. (c) 14 days**

Let 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

**Other way**:- B leaves the work 5 days before means A did work alone for that 5 days

Work Done by A in that 5 day = 5/20 = 1/4

Remaining work = 3/4

To complete the work together A+B would have
taken 1/ (1/20+ 1/30) = 600/50 = 12
days

3/4th of the work together will be completed in
12*3/4 = 9 days

Total time = 5+9 = 14 days

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