## Practice Questions – Time and Work – 1

1. A and B together can do a piece of work in 4 days. If A alone can do it 6 days, in how many days can B alone complete the same piece of work?

a) 12

b) 8

c) 9

d) 16

e) None of these

a) 12

Explanation:

(A+B)’s 1 days work=1/4

A’s 1 days work=1/6

B’s 1 days work=(1/4)-(1/6) = (3-2)/12= 1/12

B alone can complete the work in 12 days.

2. Fifty six men can complete a piece of work in 24 days. In how many days can 42 men complete the same piece of work?

a) 18 days

b) 32 days

c) 98 days

d) 48 days

e) None of these

b) 32 days

Explanation:

56×24=42×number of days,

Number of days=(56×24)/42=32

3. 15 Women can complete a work in 4 days. How long 20 women will take to complete the work?

a) 2 days

b) 2 (1/2) days

c) 3 days

d) 3 (1/2)days

e) None of these

c) 3 days

Explanation:

15×17=20×D2

Or, D2= (15×4)/20=3 days

4. Each child from a certain school can make 5 items of handicraft in a day. If 1125 handicraft items are to be displayed in an exhibition then in how many days can 25 children make these items ?

a) 6 days

b) 9 days

c) 8 days

d) 7days

e) None of these

b) 9 days

Explanation:

Required numbers of days= 1125/(5×25)=9days

5. 9 children can complete a piece of work in 360 days. 18 men can complete the same piece of work in 72 days and 12 women can complete the piece of the work in 162 days. In how many days can 4 men, 12 women and 10 children together complete the piece of work?

a) 124days

b) 81days

c) 68days

d) 96days

e) None of these

b) 81days

Explanation:

Clearly,

9×360 children =18×72men=12×162women

45childern=18 men=27women

5childern=2men=3women

Now, 4 men+ 12 women+10childern

=4 men+ 8men+4men=16men

18men can complete the work in 72 days

16 men can complete the work in = (18×72)/16=81days

6. 6 men and 8 women together can complete a piece of work in 10 days. Work done by a women in one day is equal to half the work done by a man in one days. If 10 women are working alone, in how many days will the work get complete?

a) 10 Days

b) 16Days

c) 14Days

d) Cannot be determined

e) None of these

e) None of these

Explanation:

1men=2women

6men =12women

6men +8 women=(12+8)women=20women

20 women can complete the work in 10 days

10 women can complete the work in (10×20)/10=20 days

7. A and B together can complete a task in 20 days. B and C can complete the same task in 30 days. A and C can complete a same task in 40 days. What is the respective ratio of the number of days taken by A when completing the same task alone to the number of day taken by C when completing the same task alone?

a) 2:5

b) 2:7

c) 3:7

d) 1:5

e) 3:5

d) 1:5

Explanation:

(A+B)’s 1 days work=1/20

(B+C)’s 1 days work=1/30

(C+A)’s 1 days work=1/40

2(A+B+C)’s 1 days work=((1/20)+(1/30)+(1/40))=(6+4+3)/120=13/120

(A+B+C)’s 1 days work=13/240

A’s1 days work

=(13/240)-(1/30)=(13-8)/240=5/240=1/48

C’s1 days work

(13/240)-(1/20)=(13-12)/240=1/240

Required ratio=48:240=1:5

8. If 12 boys or 15 girls can do a work in 48 days, in what time will 24 boys and 6 girls do twice the work?

a) 42Days

b) 40Days

c) 45Days

d) 30Days

e) None of these

b) 40Days

Explanation:

12boy can complete the work in 48 days

=> 1boy will take 12×48=576 days. similarly 1 girls will take 15×48=720 days. Twice the work will be completed by 1 boy in 576×2=1152 days and 1 girls by 720×2=1440 days. One day work of 24 boys and 6 girls

=(24/1152)+(6/1440)=(120+2)/5760=144/5760=1/40

They will complete the whole work in 40 day.

9. M and N can do a work in 10 days and 15 days respectively. If M starts on the work and both work alternatively day after day, in how many days will the work will be completed?

a) 10

b) 12

c) 8

d) 9

e) None of these

b) 12

Explanation:

Work done in 1st two days 1/10=1/15=(3+2)/30=1/6

Number of days =12

10. 9 children can complete a piece of work in 360 days, 18 men can complete the same piece of work in 72 days and 12 women can complete in 162 days. In how many days can 4 men, 12 women and 10 children together complete the piece of work?

a) 68 days

b) 81days

c) 96 days

d) 124 days

e) None of these

b) 81days

Explanation:

According to the question, 9×360children=18×72 men =12×162women=>5 children =2men=3women

4men+12women+10chilren

=(10+20+10)children=40 children

M1D1=M2D2

9×360=40×D2

D2=(9×360)/40=81days