**Time and Work Practice Problems Set – 2**

**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

**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

**Solutions:**

**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. (b)**

**6(2/3) days**

M1D1H1E1W2 = M2D2H2E2W1 (From MDH Rule)

Efficiency 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