Time And Work

1.P and Q together can complete a work in 6 days. Q and R together can complete the same work in 15 days. P and R together can complete the work in 20/3 days. What is the ratio of number of days that Q alone takes to complete the work to the number of days that R alone takes to complete the work?
1 : 3 : 5
2 : 1 : 4
3 : 2 : 5
4 : 2 : 3
5 : None of these
2.A and B together can complete a piece of work in 15 days, B and C together can complete the work in 20 days. A and C together can complete the work in 30 days. What is the ratio of number of days A alone takes to do the work to the number of days C alone takes to do the work?
1 : 1 : 6
2 : 1 : 3
3 : 2 : 3
4 : 3 : 2
5 : None of these
3.Two boys can do a piece of work in ten days. Three girls can do the same work in five days. In how many days can a boy and a girl together do the work?
1 : 16 days
2 : 8(4/7) days
3 : 12 days
4 : 5 (1/2)days
5 : None of these
4.Four men can complete a work in 5 days which 20 women take 20 days to complete. How many days will 6 men and 40 women together take to complete the work?
1 : 1day
2 : 4days
3 : 2 (1/2)days
4 : 3days
5 : None of these
5.A and B can complete a work in 20 days and 30 days respectively. Both of them started doing the work and A left after six days. In how many more days can B complete the remaining work?
1 : 20
2 : 10
3 : 15
4 : 12
5 : None of these

Time and work

1) If 5 women or 8 girls can do a work in 84 days. In how many days can 10 women and 5 girls can do the same work? 

A.    32 days

B.    48 days

C.    52 days

 D.    38 days

Answer : A.

Given that 5 women is equal to 8 girls to complete a work. 
So, 10 women = 16 girls. 
Therefore 10 women + 5 girls = 16 girls + 5 girls = 21 girls.
8 girls can do a work in 84 days then 21 girls can do a work in (8*84/21) = 32 days.
Therefore 10 women and 5 girls can a work in 32 days

2) If 34 men completed 2/5th of a work in 8 days working 9 hours a day. How many more man should be engaged to finish the rest of the work in 6 days working 9 hours a day? 

A.    89

B.    98

 C.    102

 D.    142

Answer : C.

From the above formula i.e (m1*t1/w1) = (m2*t2/w2)
so, (34*8*9/(2/5)) = (x*6*9/(3/5))
so, x = 136 men
number of men to be added to finish the work = 136-34 = 102 men

3) If 9 men working 6 hours a day can do a work in 88 days. Then 6 men working 8 hours a day can do it in how many days? 

A.    89 days

B.    90 days

 C.    85 days

 D.    99 days

Answer : D.
From the above formula i.e (m1*t1/w1) = (m2*t2/w2)
so (9*6*88/1) = (6*8*d/1)
on solving, d = 99 days.

4) A is twice as good a workman as B and together they finish a piece of work in 18 days. In how many days will A alone finish the work? 

A.    31 days

 B.    25 days

 C.    27 days

D.    29 days

Answer : C.

If A takes x days to do a work then B takes 2x days to do the same work.
--> 1/x+1/2x = 1/18
--> 3/2x = 1/18
--> x = 27 days.
Hence, A alone can finish the work in 27 days.

5) Worker A takes 8 hours to do a job. Worker B takes 10 hours to do the same job. How long it take both A & B, working together but independently, to do the same job? 

A.    40/9 days

 B.    40/7 days

C.    7.5 days

D.    8.5 days

Answer : A.
: A's one hour work = 1/8. 
B's one hour work = 1/10. 
(A+B)'s one hour work = 1/8+1/10 = 9/40. 
Both A & B can finish the work in 40/9 days

Time and Work

1. P is able to do a piece of work in 15 days and Q can do the same work in 20 days. If they can work together for 4 days, what is the fraction of work left?
A. 8/15	B. 7/15
C. 11/15	D. 2/11

Answer : Option A

Explanation :

Amount of work P can do in 1 day = 1/15

Amount of work Q can do in 1 day = 1/20

Amount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60

Amount of work P and Q can together do in 4 days = 4 × (7/60) = 7/15

Fraction of work left = 1 – 7/15= 8/15

2. P can lay railway track between two stations in 16 days. Q can do the same job in 12 days. With the help of R, they completes the job in 4 days. How much days does it take for R alone to complete the work?
A. 9(3/5) days	B. 9(1/5) days
C. 9(2/5) days	D. 10 days

Answer : Option A

Explanation :

Amount of work P can do in 1 day = 1/16

Amount of work Q can do in 1 day = 1/12

Amount of work P, Q and R can together do in 1 day = 1/4

Amount of work R can do in 1 day = 1/4 - (1/16 + 1/12) = 3/16 – 1/12 = 5/48

=> Hence R can do the job on 48/5 days = 9 (3/5) days

3. P, Q and R can do a work in 20, 30 and 60 days respectively. How many days does it need to complete the work if P does the work and he is assisted by Q and R on every third day?
A. 10 days	B. 14 days
C. 15 days	D. 9 days

Answer : Option C

Explanation :

Amount of work P can do in 1 day = 1/20

Amount of work Q can do in 1 day = 1/30

Amount of work R can do in 1 day = 1/60

P is working alone and every third day Q and R is helping him

Work completed in every three days = 2 × (1/20) + (1/20 + 1/30 + 1/60) = 1/5

So work completed in 15 days = 5 × 1/5 = 1

Ie, the work will be done in 15 days