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QUESTION: 1

A and B alone can do a piece of wok in 8 and 18 days respectively. In how many days the work will be completed if they both work on alternate days starting with B?

Solution:

A = 8 days, B = 18 days

Total work = LCM(8,18) = 72

So efficiency of A = 72/8 = 9, efficiency of B = 72/18 = 4

2 days work of (A+B) = 9+4 = 13

2*5(10) days work of (A+B) = 9+4 = 13*5 = 65

So remaining work = 72-65 = 7

Now A’s turn on 6th day, he will do remaining work(7) in 7/9 day

So total

QUESTION: 2

A, B and C can all together do piece of work in 10 days, in which B takes three times as long as A and C together do the work and C takes twice as long as A and B together take to do the work. In how many days B can alone do the work?

Solution:

(A+C) in x days so B completes in 3x days

then (1/x) + (1/3x) = 1/10

solve, x = 40/3

so B in 3x = 3*(40/3)= 40 days

OR

Given A+B+C = 10 and that B takes 3 times as A+C, so A+C is three times stronger than B

So this means that 4 times stronger can do work in 10 days

So 1 time stronger(B) in 4*10 = 40 days

QUESTION: 3

20 men can complete a piece of work in 14 days. 7 men started the work and after 20 days, 7 more men joined the work. In how many days the remaining work will be completed?

Solution:

Let (7+7) complete remaining work in x days.

So 20*14 = 7*20 + 14*x

x = 10 days

QUESTION: 4

20 men can complete a work in 14 days and 20 women can complete the same work in 18 days. 7 men and 9 women started the work. After working for some days, they were replaced by 10 men and 10 women who complete the remaining work in 9 days. How much work was completed by initially employed men and women?

Solution:

20 m in 14 days so 10 men in (20*14)/10 = 28 days

20 w in 18 days so 10 women in (20*18)/10 = 36 days

So (1/28 + 1/36)*9 = 4/7

So 1 – 4/7 = 3/7 work was done by 7 men and 9 women

QUESTION: 5

A, B and C can alone complete a work in 10, 12 and 15 days respectively. A and C started the work and after working for 4 days, A left and B joined. In how many days the total work was completed?

Solution:

(A+C) = (1/10 + 1/15) = 1/6. They worked for 4 days so did (1/6)*4 = 2/3rd of work

Remaining work = 1 – 2/3 = 1/3

Now A left , B and C working

(B+C) = (1/12 + 1/15) = 9/60 = 3/20. They worked for x days and completed 1/3rd of work so (3/20)*x = 1/3, so x = 20/9 days

Total = 4 + 20/9

QUESTION: 6

A, B and C can alone complete a work in 10, 12 and 15 days respectively. All started the work but B left the work 3 days before completion. How much work was then done by A and B together in the total work?

Solution:

Let work completed in x days, so A and C worked for all x days, and B for (x-3) days.

So

(1/10 + 1/15)*x + (1/12)*(x-3) = 1

Solve, x = 5 days

In 5 days, A did 5/10 = 1/2 of work

In (5-3) = 2 days, B did 2/12 = 1/6 of work

So total by A and B = (1/2 + 1/6) = 2/3

QUESTION: 7

2 men and 3 women can together complete a piece of work in 4 days and 3 men and 2 women together can complete work in 3 days. In how many days 10 women will complete this work?

Solution:

2m + 3w = 4, 3m + 2w = 3

So 4(2m + 3w) = 3(3m + 2w)

8m + 12w = 9m + 6w

6w = 1m

Given 2m + 3w = 4, so 2*(6w) + 3w = 4, so 15 women in 4 days, so 10 women in (15*4)/10 = 6 days

QUESTION: 8

A alone can complete a work in 5 days more than A+B together and B alone can complete a work in 45 days more than A+B together. Then in how many days A and B together can complete the work?

Solution:

Shortcut = √5×45 = 15

OR

Let (A+B) can do in x days, so

1/(x+5) + 1/(x+45) = 1/x

Solve, x^{2} = 225, x = 15

QUESTION: 9

20 men can complete a work in 14 days and 20 women can complete the same work in 18 days. 8 men start the work and after working for 21 days, they are replaced by x women. If the remaining work is to be completed by x women in 9 days, then how many women should be employed?

Solution:

20 m in 14 days so 8 men in (20*14)/8 = 35 days

In 21 days 8 men complete (1/35)*21 = 3/5 work

Remaining work = 1 – 3/5 = 2/5

20 women do 1 work in 18 days so x women will do 2/5 work in 9 days

10*(2/5)*18 = x*1*9

QUESTION: 10

A alone can complete a work in 21 days. If B is 40% more efficient than A, then in how many days A and B together can complete the work?

Solution:

Let efficiency of A is x, so of B = (140/100)*x = 7x/5

So ratio of efficiencies = x : 7x/5 = 5 : 7

So ratio of days = 7 : 5

A can do in 21 days, so 7y = 21, y = 3

So B can do in 5*3 = 15 days

A+B in (21*15)/(21+15) = 8 � days

QUESTION: 11

A project manager hired 16 men to complete a project in 40 days. However after 30 days he realized that only 4/9 th of the work is complete. How many more men does he need to hire to complete the project on time ?

Solution:

16*30 / 4/9 = M * 10/5/9

16*30*9/ 4 = M *10*9/5

1080 = 18M

M = 1080/18 = 60

Men required = 60 – 16 = 44

QUESTION: 12

20 men can complete a piece of work in 15 days and 12 women can complete the same piece of work in 24 days. What is the ratio of amount of work done by 30 men in oneday to the amount of work done by 16 women in 1 day ?

Solution:

M : W = 30/20*15 : 16/12*24

= 1/10 : 1/ 18 = 1/5:1/9

Ratio = 9:5

QUESTION: 13

X alone can do a piece of work in 5 days. Y can do the same piece of work in 4 days. X and Y are assigned to do the work for Rs.5000.They complete the work in 2 days with the help of Z. How much is to be paid to Z ?

Solution:

Z’s one day work = ½ – [ 1/5+1/4] = 10-4+5/20 = 1/20

Ratio = 1/5:1/4:1/20 = 4/20 : 5/20 : 1/20 = 4:5:1

Z = 5000*1/10 = 500

QUESTION: 14

9 men and 12 women can complete the job in 12 days.In how many days can 3 men and 4 women finish the same job working together ?

Solution:

9m+12w = 1/12

3m+4w = ?

3(3m+4w) = 1/12

3m+4w = 1/36

QUESTION: 15

P takes 6 days less than Q to finish the work individually. If P and Q working together complete the work in 4 days, then how many days are required by Q to complete the work alone ?

Solution:

= 1/6 + 1/12

= 2+1/12 =3/12 = 1/4

QUESTION: 16

If X, Y and Z can complete a work in 6 days. If X can work twice faster than Y and thrice faster than Z, then the no of days Z alone can complete the work is

Solution:

1/x+1/2x+1/3x = 1/6

6+3+2/6x = 6

11/6x = 6

X = 11

Z = 3x = 33

QUESTION: 17

If 20 men can do a piece of work in 42 days working 8 hours per day then how many men are required to complete the work, working 5 hours per day in 33 days ?

Solution:

M = 20*42*8/5*33 = 40.72 = 41

QUESTION: 18

Three men, four women and six children can complete a work in 7 days. A woman does double the work a man does and a child does half the work a man does. How many women alone can complete this work in 7 days ?

Solution:

2 men = 1 woman

1 man =1/2 woman

3 men =3/2 women

2 children = 1 man =1/2 woman

1 child =1/4 woman

6 children =6/4 =3/2 women

Now, three men, four women and six children

=3/2 + 4 +3/2 =3+8+3/2 = 14/2 = 7 women

QUESTION: 19

If A can complete a work in 30 days, B can do the same work in 36 days, If after doing 5 days, leaves the work.Find in how many days B will do the remaining work ?

Solution:

A = 1/30, B = 1/42

6 days work = 5*1/30 = 1/6

Remaining = 5/6

B = 5*36/6 = 30

QUESTION: 20

P is 20 % more efficient than Q, how much time will they working together take to complete a job which P alone could have done in 20 days ?

Solution:

P : Q = 100 : 120

10/12 = 20/x

12/10 = x/20

X = 24

Q = 1/24 or 20*120/100 = 24

P+Q = 1/20 + 1/24

= 24+20/480 = 44/480 = 10.91 = 11 days

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