Time & Work Mock #01


  1. If 12 men and 16 boys can do a piece of work in 10 days and 18 men and 50 boys can do it in 5 days. Compare the efficiency of a man to that of a boy.
  1. 1 : 1
  2. 2 : 1
  3. 1 : 2
  4. 3 : 1

2.   12 men can complete a work in 9 days. 3 days after they started the work, 2 men left and 8 joined. How many days will it take to complete the remaining work?

  1. 2 days
  2. 3 days
  3. 4 days
  4. 5 days

  3. A tank can be filled by pipe A in 6 hours and pipe B in 2 hours. At 2 pm, pipe B was opened. At what time will the tank be filled if pipe A is opened at 2: 30 pm?

  1. 3.00 pm
  2. 3.30 pm
  3. 3.15 pm
  4. 2.45 pm

4. A swimming pool has 3 drain pipes. The first two pipes A and B, operating simultaneously, can empty the pool in half the time than that of taken by C alone. Pipe A, working alone, takes half the time taken by pipe B. Together they take 6 hrs 40 minutes to empty the pool. Time taken by pipe A to empty the pool, in hours, is

  1. 10
  2. 15
  3. 30
  4. 7

5. A tap can fill a cistern in 40 minutes and a second tap can empty the filled cistern in 60 minutes. By mistake without closing the second tap, the first tap was opened. In how many minutes will the empty tank be filled ?

  1. 72
  2. 84
  3. 108
  4. 120

6. If the work done by (x – 1) men in (x + 1) days and the work done by (x + 2) men in (x – 1) days is in the ratio of 9: 10, then x is equal to.

  1. 5
  2. 6
  3. 7
  4. 8

7. A and B can separately do a piece of work in 20 and 15 days respectively. They worked together for 6 days. After that B was replaced by C. The work was Finished in next 4 days. The number of days in which C alone could do the work is –

  1. 35 days
  2. 30 days
  3. 45 days
  4. 40 days

8.A and B together can finish a job in 10 days while B and C together can do it in 18 days. A started the job and worked for 5 days, then B worked for 10 days and the remaining job was finished by C in 15 days. In how many days could C alone have finished the whole job?

  1. 30 days
  2. 15 days
  3. 45 days
  4. 24 days

9. C is twice as efficient as A, B takes thrice as many days as C. A takes 12 days to finish the work alone. If they work in pairs (ie, AB, BC, CA) starting with AB on the first day, B C on the second day and AC on the third day and so on, they how many days are required to finish the work?

  1. 6 1/5  days
  2. 4.5  days
  3. 5  1/9 days
  4. 8 days

10.Three pipes A, B and C can fill a tank in 20 min, 10 min, and 30 min respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions x, y and z respectively. The proportion of solution y in the liquid in the tank after 3 min is.

  1. 6/11
  2. 7/11
  3. 8/11
  4. 5/11

Correct Answers

  1. Option D.

12M + 16B = 10 days … (i)

18M + 50B = 5 days

= 9M + 25B = 10 days … (ii)

From (i) & (ii)

We have

12M + 16B = 9M + 25B

3M = 9B

1M = 3B

So, Efficiency of a man to that of a boy = 3 : 1

 

  1. Option C. 4 days
  2. A = 6 hr  , B = 2hr

Let the capacity of tank = 12 litres

Rate of filling of tank by pipe A = 12/6  = 2 litre per hour

and rate of filling of tank by pipe B =  12/2  = 6 litre per hour

  • Rate of filling of tank by pipe A & B together = 8 litre per hour

Now, Pipe B was opened ½  hour earlier than pipe A.

Volume of tank filled by pipe B in  ½ hour = 3 litre

 

-Remaining part of the tank which is still empty = (12 – 3) litre = 9 litre

Time required to fill 9 litre of tank by pipe A & B together = 9/8 hr = 1 hr 7.5 min

Required point of time = 2 : 30 pm + 1 hour 7.5 mins = 3 : 37.5 pm

 

  1. Option B.

Let- hour = time taken by pipe A alone to empty the pool

2x hr. = time taken by pipe B alone to empty the poo

  1. Option D.

Required time = 60 × 40 / 60-40 = 2400/20  =120 min.

 

  1. Option D.

(x-1)  (x+1)  / ( x+2)  (x-1)  = 9/10

             10x + 10 9x + 18 = 8

 

  1. Option D.

A   20                   3

60

B   15                     4

_

7

Work done by  (A+B)  in 6 days  = 7 × 6 = 42

Work done by  (A+C)  in 4 days  = 60-42 = 18

Work done by  A  in 4 days  =  3 × 4 = 12

So, Work done by  C  in 4 days  = 18-12 = 6

So, time taken by C alone to complete the work =  4/6  × 60  = 40 days

 

8.Option C.

( A + B )’s 5 day work +  (B+C)’s  5 days’ work = 1

5/10 +  5/18 + 10/x  =  1

X = 45 days

 

9.Option C.

A  :  B :  C

Effi. =             3 :  2  :  6

No of days = 2 :  3  :  1

No of days taken by A = 12

No of days taken by B = 18

No of days taken by C = 6

1 day work of A+B =  5/36

1 day work of B+C= 8/36

1 day work of C+A= 9/36

Days 1 2 3 4 5 6
1 days’ work 5/36 8/36 9/36 5/36 8/36 9/36

 

No of days taken by AC for the rest of the work = 1/36  ÷ 9/36 = 1/9

So total time taken to complete the work= 5 + 1/9  = 5 1/9 days

10.Option A.

Filling done by all 3 pipes  in 3 min  =  3/20  +  3/10  + 3/30  = 11/20

Filling done by 2nd pipe in 3 min  = 3 /10

So , required  ratio = 3/10  ̸  11/20 =  6/11 .

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